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find abc when a\(b+8), a\(b^2 - 1), c\(b^2 - 1), b + c = a^2-1, primes a,b,c

Source: KJMO 2009 p1

May 2, 2019
number theorymultipleProductprimes

Problem Statement

For primes a,b,ca, b,c that satis fy the following, calculate abcabc. ∙\bullet b+8b + 8 is a multiple of aa, ∙\bullet b2−1b^2 - 1 is a multiple of aa and cc ∙\bullet b+c=a2−1b + c = a^2 - 1.
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