# If $p$ and $q$ are co-prime numbers,

Question:

If $p$ and $q$ are co-prime numbers, then $p^{2}$ and $q^{2}$ are

(a) coprime

(b) not coprime

(c) even

(d) odd

Solution:

We know that the co-prime numbers have no factor in common, or, their HCF is 1.

Thus, $p^{2}$ and $q^{2}$ have the same factors with twice of the exponents of $p$ and $q$ respectively, which again will not have any common factor.

Thus we can conclude that $p^{2}$ and $q^{2}$ are co-prime numbers.

Hence, the correct choice is (a).