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Additive property of a multiplicative function

Source: VJIMC 2022 Category II P4

April 9, 2022
functionnumber theoryVJIMC

Problem Statement

Let gg be the multiplicative function given by g(pα)=αpα−1,g(p^{\alpha}) = \alpha p^{\alpha-1}, for all α∈Z+\alpha\in\mathbb Z^+ and primes pp. Prove that there exist infinitely many integers nn such that g(n+1)=g(n)+g(1).g(n+1) = g(n) + g(1).
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