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\sigma(p^2)=\sigma(q^b)

Source: Mathcenter Contest / Oly - Thai Forum 2008 R2 p7 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 11, 2022
number theorysum of divisors

Problem Statement

For every positive integer nn, σ(n)\sigma(n) is equal to the sum of all the positive divisors of nn (for example, σ(6)=1+2+3+6=12\sigma(6)=1+2+3+6=12) . Find the solution of the equation σ(p2)=σ(qb)\sigma(p^2)=\sigma(q^b) where pp and qq are primes where p>q and bb are positive integers.
(gools)
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