MathDB

1 mod 2009^(2009)

Source:

November 12, 2009

modular arithmeticnumber theorynumber theory proposed

Problem Statement

Let A\equal{}\{n: 1 \le n \le 2009^{2009},n \in \mathbb{N} \} and let S\equal{}\{n: n \in A,\gcd \left(n,2009^{2009}\right)\equal{}1\}. Let

P

be the product of all elements of

S

. Prove that

P \equiv 1 \pmod{2009^{2009}}.

Nanang Susyanto, Jogjakarta