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  4. For any integer a, the remainder obtained when a2 is divided by 4 is

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Q. For any integer $a$, the remainder obtained when $a^{2}$ is divided by $4$ is

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Solution:

Here $a=2 n$ or $a=2 n+1$.
$\therefore a^{2}=4 n^{2}$ ( this is divisible by $4$ )
or $a^{2}=(2 n+1)^{2}=4 n^{2}+4 n+1$.
(This leaves the remainder $1 $ when divided by $4$ )