Number theory · Primes · Congruences · Quadratic residues · Parity
Find all prime numbers \(p\), \(q\) and \(r\) for which the number
\[ p^{\,q+r} + q^{\,p+r} + r^{\,q+p} \]
is the square of an odd natural number.
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian Regional Competition (Okruzno takmicenje) 2024, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source