If $y\equiv 1 mod 4$ then $y^2 \equiv 1 mod 8$

Question

Given $$ y\equiv 1\ mod \ 4 $$ How can i proove that $$ y^2\equiv1\ mod\ 8 $$

Answer 1

Let $y=4k + 1$ hence $y^2 = 16k^2 + 8k + 1$