Number theory · Divisor sum · Sigma function · Prime factorization · Multiplicative functions
Prove that there exist infinitely many pairs \((m, n)\) of distinct positive integers such that the sum of all positive divisors of \(m^2\) is equal to the sum of all positive divisors of \(n^2\).
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian National Competition (Drzavno takmicenje) 2019, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source