I have that $2^{947} (\bmod 1373)$ how does one solve this without a calculator? Can you separate it into nice $2^x2^y$ or $(2^x)^y$? I'm really not sure how to go about this problem. Thanks for any help!
2026-03-27 21:43:26.1774647806
$2^{947} (\bmod 1373)$
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General strategy: You never need large numbers if you reduce as you go along. Since $$ 2^{10} = 1024 \equiv -349 \pmod {1373} $$ you have a good start. Squaring $349$ will tell you $2^{20}$, and so on.