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a_p / b_p = 1 +1/2+ .. +1/(p^2 -1)

Source: 2014 Saudi Arabia GMO TST I p2

July 26, 2020
number theorygreatest common divisorGCD

Problem Statement

Let p≥2p \ge 2 be a prime number and apbp=1+12+..+1p2−1\frac{a_p}{b_p}= 1 +\frac12+ .. +\frac{1}{p^2 -1}, where apa_p and bpb_p are two relatively prime positive integers. Compute gcd (p,bp)(p, b_p).
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