MathDB

2

Part of 2000 Singapore MO Open

Problems(1)

240 divides all numbers of the form p^4 - q^4 when p,q primes >5

Source: Singapore Open Math Olympiad 2000 2nd Round p2 SMO

4/2/2020
Show that 240240 divides all numbers of the form p4−q4p^4 - q^4, where p and q are prime numbers strictly greater than 55. Show also that 240240 is the greatest common divisor of all numbers of the form p4−q4p^4 - q^4, with pp and qq prime numbers strictly greater than 55.
dividesdivisibleprimesnumber theoryGCD