9. How many multiples of 7, between 1 and 6000, are squares of integers?
(A) 9
(B) 20
(C) 77
(D) 11
(E) 122
(9) The correct answer is $(D)$.

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 $49 n^{2} \leq 6000$, it is necessary that $n \leq 11$. The numbers sought are thus 11, those obtained with the expression $49 n^{2}$ for $1 \leq n \leq 11$.

Question proposed by Paolo Francini.