How do we find the remainder of the division $2^{1990}/1990$? I actually tried it through Fermat's theorem but couldn't arrive at the answer directly.
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1http://math.stackexchange.com/questions/545759/what-is-the-remainder-when-21990-is-divided-by-1990 – lab bhattacharjee Dec 22 '13 at 04:32
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You might want to try using Fermat's Little Theorem along with the Chinese Remainder Theorem. – Avi Steiner Dec 22 '13 at 04:47
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Well, since 1990 is not prime, you might want to look into Euler's Theorem, which extends Fermat's Little Theorem.
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Euler's Theorem isn't applicable as-is - $2$ and $1990$ are not coprime. There is another theorem you can use to help with this, though.. hint – Thomas Dec 22 '13 at 04:43