how to use congruent modulos to find remainders....like for suppose...find the remainder

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Blazing goIITian

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From Euler's totient theorem

$3^{phi{100}}equiv01mod100$

$3^{40}equiv01mod100$

So, $3^{4000}equiv01mod100$

[IMG]http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/0/6/3/0638cc54ee34d87aa803d78fe3ec072aa8749bf5.gif[/IMG] :)

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