3

Part of 2017 Israel Oral Olympiad

Problems(1)

Differences of Powers of Primes p^q-q^p

Source: Israeli Oral Olympiad #3

2017 prime numbers

p_1,...,p_{2017}

are given. Prove that

\prod_{i<j} (p_i^{p_j}-p_j^{p_i})

is divisible by 5777.

number theoryprimeprime numbers