MathDB
f(m,k) run over N

Source: China second round 2007 p3

March 10, 2012
functionnumber theory proposednumber theorynumber theory unsolved

Problem Statement

For positive integers k,mk,m, where 1≤k≤51\le k\le 5, define the function f(m,k)f(m,k) as f(m,k)=∑i=15[mk+1i+1]f(m,k)=\sum_{i=1}^{5}\left[m\sqrt{\frac{k+1}{i+1}}\right] where [x][x] denotes the greatest integer not exceeding xx. Prove that for any positive integer nn, there exist positive integers k,mk,m, where 1≤k≤51\le k\le 5, such that f(m,k)=nf(m,k)=n.
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