2

Part of 2006 Junior Tuymaada Olympiad

Problems(1)

difference of 16th powers of 2 odd primes to be divisible by 8 odd primes

Source: Tuymaada Junior 2006 p2

Ten different odd primes are given. Is it possible that for any two of them, the difference of their sixteenth powers to be divisible by all the remaining ones ?

number theorypower of numberpowersprimes