PUMaC 2016 · 数论（B 组） · 第 2 题
PUMaC 2016 — Number Theory (Division B) — Problem 2
题目详情
- For a positive integer n , let s ( n ) be the sum of the digits of n . If n is a two-digit positive n integer such that is a multiple of 3, compute the sum of all possible values of n . s ( n )
解析
- If is a multiple of 3 then n is a multiple of 3, so s ( n ) is a multiple of 3, which means that s ( n ) n is a multiple of 3 s ( n ), so n is a multiple of 9, which means that s ( n ) is a multiple of 9, which means that n is a multiple of 27. Checking n = 27, n = 54, and n = 81, we find that all of these values satisfy the stated condition, so the answer is 27 + 54 + 81 = 162 . Problem written by Eric Neyman.