For any positive integer $n$,the last digit of $5^n$ is always.......

Prove that $21^{n}$ cannot end in zero for any natural number $n \in N$.

Express $5005$ as a product of prime factors.

If a positive integer is of the form $3q + 1$,where $q$ is a natural number,then its square can be written in the form $3m + 1$. Is the statement true or false?

Show that the square of an odd positive integer is of the form $8m+1$ for some whole number $m$.

Write whether the square of any positive integer can be of the form $3m + 2$,where $m$ is a natural number. Justify your answer.