Introduction to Number Theory links & errata

Below are some of the links that are referenced in the book Introduction to Number Theory. (Note: Art of Problem Solving is not responsible for the content on any external site.)

How to Use This Book

Chapter 11

Links to solutions for interesting problems at the end of the chapter.

Unfortunately, the book is not perfect. Here is a list of the known errors. If you know of an error not on this list, we would appreciate a short email to books@artofproblemsolving.com describing the error.

Errata - Second Edition (those in red are corrected in the 2013 printing)

• On page 55, the second bullet point should begin, "Since a common divisor of 990 and 720 is also a divisor of 270"
• Text, page 148, problem 8.3.3 should have a period at the end of the problem.
• Text, page 184, problem 10.2.6: should say "...Its units digit is 3."
• Text, page 187: section 10.4 should be titled "Units Digits Everywhere!"
• Text, page 234, second set of equations in the solution to Problem 12.13 (after "Now, note each of the following:"): there should not be an m in the middle parts of the two equations.
  
• Text, page 253, the four congruences near the top of the page that are mod 9 should be mod 11.
• Text, page 262, problem 14.5: should by modulo-60 in the first line.
• Solutions, page 54, problem 6.38, the first inequality should be ≤, not < (because p might be 2) -- the second inequality is still < so the solution is still correct.
• Solutions, page 63, Problem 8.3.1, parts (c) and (d) should show base 8.
• Solutions, page 77, Problem 9.3.1, part (f), the answer should be B1A.
• Solutions, page 98, Problem 11.22, part (i), the answer should be -24/7.
• Solutions, page 99, Problem 11.25, part (g), the answer should be 0.01176470588235294 (the part in bold is repeating).
• Solutions, page 132, Problem 15.22: the answer is correct, but the first paragraph of the explanation is not. It is not clear that the larger number cannot be 2 times the smaller number, but this can be shown by a brute-force computation.
• Solutions, page 133, Problem 15.26: a step is missing in the computation:
  ... = (1,000 + 24)^2 = 1,000^2 + 2 * 1,000 * 24 + 24^2 = 1,000,000 + 48,000 + 576 = ...
• Solutions, page 136, Problem 15.42: The original problem asks for the cube root of the given expression, while the solution solves for the square root. The answer should be 781250.
• Solutions, page 138, Problem 15.51: The final answer is correct, but the reasoning at the end of the solution is slightly off. Since we want the two smallest values of N that are greater than 1, we must take m=1 and m=2, giving the difference (27720 * 2 + 1) - (27720 * 1 + 1) = 27720.

Errata - First Edition

• On page 53, on problem 3.6.1, The first sentence in the problem states that "7 | 4" whereas it should state "7 | 42."
• On page 55, the second bullet point should begin, "Since a common divisor of 990 and 720 is also a divisor of 270"
• On page 67, the factor trees for problem 4.5 show the number 325 at the top instead of 375, though the rest of the branches are correct.
• Section 6.2, around page 111: the discussion confuses Mersenne primes with Fermat primes. Mathematicians are not currently finding new Fermat primes, and indeed it is conjectured that there aren't any more to find. On the other hand, a new largest Mersenne prime is found every year or so.
• Text, page 248, Problem 13.6 part (e) should be mod 11, not mod 9
• Text, page 253, the four congruences near the top of the page that are mod 9 should be mod 11.
• Solutions, page 63, Problem 8.3.1, parts (c) and (d) should show base 8.
• Solutions, page 77, Problem 9.3.1, part (f), the answer should be B1A.
• Solutions, page 136, Problem 15.42. The original problem asks for the cube root of the given expression, while the solution solves for the square root. The answer should be 781250.