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  4. The remainder when (3232)32 is divided by 7, is

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Q. The remainder when $(32^{32})^{32}$ is divided by $7$, is

Binomial Theorem

Solution:

$(32^{32})^{32} = 32^{1024} = (28 + 4)^{1024}$
$= 4 +$ a multiple of $28$.
$= 4 +$ a multiple of $7$.