Number theory · Divisibility · Bounding arguments · Parity · Cyclic symmetry · Casework
How many triples \((a, b, c)\) of positive integers are there such that \(2a + 1\) is divisible by \(b\), \(2b + 1\) is divisible by \(c\), and \(2c + 1\) is divisible by \(a\)?
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian Republic Competition (Republicko takmicenje) 2004, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source