14. How many multiples of 7, between 1 and 5000, are squares of integers?
(A) 10
(B) 26
(C) 12
(D) 102
(E) 70
(14) The correct answer is $(A)$.

A perfect square is a multiple of 7 if and only if it is of the form $(7 n)^{2}=49 n^{2}$, where $n$ is an integer. To have $49 n^{2} \leq 5000$, it is necessary that $n \leq 10$. The numbers sought are thus 10, those obtained with the expression $49 n^{2}$ for $1 \leq n \leq 10$.

Question proposed by Paolo Francini.