Number theory · Squarefree numbers · Divisor structure · Prime factorisation · Case analysis · Counting
In how many ways can natural numbers \(a\), \(b\), \(c\) be chosen so that all of the following hold?
\[ 1^{\circ} \quad a < b < c < 52 ; \]
\[ 2^{\circ} \quad a \mid c ; \qquad 3^{\circ} \quad b \mid c ; \]
\[ 4^{\circ} \quad \text{neither } a \text{ nor } b \text{ is divisible by the square of a natural number greater than } 1 ; \]
\[ 5^{\circ} \quad c \text{ is divisible by the square of a natural number greater than } 1 . \]
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian National Competition (Drzavno takmicenje) 2008, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source