MathDB
Nice Number Theory

Source: 2020 RMM Shortlist N2

October 8, 2022
number theoryPerfect SquaresRMMRMM 2020RMM Shortlist

Problem Statement

For a positive integer nn, let φ(n)\varphi(n) and d(n)d(n) denote the value of the Euler phi function at nn and the number of positive divisors of nn, respectively. Prove that there are infinitely many positive integers nn such that φ(n)\varphi(n) and d(n)d(n) are both perfect squares.
Finland, Olli Järviniemi
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