MathDB
k=m+2mn+n iff 2k+1 composite (Slovenia 1997 1st Grade P1)

Source:

May 2, 2021
number theory

Problem Statement

Let kk be a positive integer. Prove that: (a) If k=m+2mn+nk=m+2mn+n for some positive integers m,nm,n, then 2k+12k+1 is composite. (b) If 2k+12k+1 is composite, then there exist positive integers m,nm,n such that k=m+2mn+nk=m+2mn+n.
Back to ProblemsView on AoPS