又是一道没在ＰＲＥＰ讨论贴里找到的题目

If n is a multiple of 5 and n=p^2q(P的平方乘以Q)，where p and q are prime numbers, which of the following must be a multiple of 25?

P^2

q^2

pq

p^2q^2

p^3q

what is the solution?

if  n is a multiple of 5, then either p is a multiple of 5 or q is a multiple of 5 or both

p^2 => no if only q is a multiple of 5

q^2 => no if only p is a multiple of 5

pq => no if only q is a multiple of 5

p^2q^2 => guaranteed to be a multiple of 25

p^3q => no if only q is a multiple of 5

I think it's D.

thank you the person who answered my question