MathDB

N2

Part of 2020 Romanian Master of Mathematics Shortlist

Problems(1)

Nice Number Theory

Source: 2020 RMM Shortlist N2

10/8/2022
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
number theoryPerfect SquaresRMMRMM 2020RMM Shortlist