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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

April 2, 2020
dividesdivisibleprimesnumber theoryGCD

Problem Statement

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.
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