Number theory · Primes · Parity · Pigeonhole · Symmetry
Let \(a\), \(b\), \(c\) be positive integers such that all three of the numbers
\[ p = b^{c} + a, \qquad q = a^{b} + c, \qquad r = c^{a} + b \]
are prime. Prove that two of the numbers \(p\), \(q\), \(r\) are equal to each other.
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian Municipal Competition 2004, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source