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Number Theory: Structures, Examples, and Problems

Number Theory: A Problem-Solving Approach

Penned By Titu Andreescu
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Number Theory: Structures, Examples, and Problems

Number Theory: A Problem-Solving Approach

Penned By Titu Andreescu
4.85 96,309 Ratings
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Editor's Note:
This introductory textbook takes a problem-solving approach to number theory, situating each concept within the framework of an example or a problem for solving. Starting with the essentials, the text covers divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Included are sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems. By emphasizing examples and applications the authors motivate and engage readers.

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Length N/A Pages
Released October, 2006
Identifier (ISBN) 1484781
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Titu Andreescu
The Mind Behind the Work
Titu Andreescu

Titu Andreescu writes contemporary fiction and has always been fascinated by character-driven stories. They hold a degree in English Literature and previously worked as an editor before transitioning to writing their own books. Titu Andreescu lives with their spouse and a very vocal rescue cat.

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Joshua Mitchell
Joshua Mitchell August 11, 2024
"I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers."
Andrew Carter
Andrew Carter April 07, 2024
"Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author."
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Michelle Lee
Michelle Lee June 01, 2025
"A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall."
Linda Wilson
Linda Wilson April 24, 2025
"Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars."
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Laura Lopez June 11, 2025
"Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars."
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Barbara Jones November 09, 2025
"Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author."
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Dorothy Smith July 03, 2025
"Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author."
Kevin King
Kevin King November 03, 2024
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James Rodriguez May 30, 2025
"I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend."
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"Not entirely to my refined tastes. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars."
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"Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre."
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"Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author."
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"I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers."
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"I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend."
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"Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author."
Mary Hall
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"Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading."
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"Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
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Jessica Thomas
Jessica Thomas June 12, 2025
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"Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers."
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"I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel."
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"A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars."
Barbara Rivera
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"Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author."
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"Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre."
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"Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars."
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"Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem."
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"Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading."
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Sharon Robinson July 21, 2025
"A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel."
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"Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre."
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"Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem."
Brian Clark
Brian Clark January 05, 2024
"Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem."
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Karen Jones October 29, 2024
"A very strong entry. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall."
Donald Green
Donald Green July 01, 2024
"A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading."
Mark Taylor
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"Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece."
Betty Wilson
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"Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem."
Kenneth Jones
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"Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me."
Richard Williams
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"Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading."
Barbara Collins
Barbara Collins September 11, 2024
"Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem."
Andrew Young
Andrew Young January 05, 2025
"A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem."
Joshua Taylor
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"Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me."
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"I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece."
Nicholas Thomas
Nicholas Thomas July 04, 2025
"Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author."
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"Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars."
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"I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece."
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"Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
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"Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre."
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"Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece."
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"A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre."
Barbara Harris
Barbara Harris January 29, 2025
"A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre."
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"A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre."
Karen King
Karen King December 27, 2025
"Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars."
Charles Smith
Charles Smith October 31, 2024
"Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author."
William  Davis
William Davis June 22, 2024
"Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece."
Jennifer Turner
Jennifer Turner August 26, 2024
"A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend."
Jennifer Rivera
Jennifer Rivera August 02, 2024
"Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall."
Donna Wilson
Donna Wilson August 14, 2024
"Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend."
Cynthia Torres
Cynthia Torres September 12, 2025
"A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem."
Ryan King
Ryan King January 16, 2025
"Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece."
Eric Wright
Eric Wright April 19, 2024
"I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre."
Elizabeth Robinson
Elizabeth Robinson May 03, 2025
"I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend."
Amanda Turner
Amanda Turner March 17, 2025
"A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre."
Paul  Parker
Paul Parker June 15, 2025
"Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars."
Ashley Allen
Ashley Allen July 21, 2024
"Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading."
Jennifer Hill
Jennifer Hill January 24, 2025
"I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece."
Dorothy Taylor
Dorothy Taylor March 30, 2025
"Not entirely to my refined tastes. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perhaps more aligned with a different audience's tastes."
Kevin Robinson
Kevin Robinson January 18, 2024
"Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers."
Cynthia Rodriguez
Cynthia Rodriguez May 23, 2025
"Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem."
Daniel Diaz
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"Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers."
Andrew Rodriguez
Andrew Rodriguez March 19, 2024
"Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem."
Matthew Moore
Matthew Moore March 24, 2025
"Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel."
Melissa Martinez
Melissa Martinez September 04, 2024
"Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall."
Nicholas Jackson
Nicholas Jackson May 04, 2024
"Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend."
James Rodriguez
James Rodriguez July 13, 2024
"I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem."
John Nelson
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"A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers."
Elizabeth Thomas
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"A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem."
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"A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author."
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Melissa Allen October 22, 2025
"Not entirely to my refined tastes. It verged on repetitive in the second act. A more concise edit would have served it well. Perfectly average."
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"Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem."
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