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I am trying to solve this modular arithmetic problem but the numbers are large. How would I simplify?

$M \equiv (1567)^{5}$ mod $2881$

jacopoburelli
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Router Power
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  • Welcome to MSE. Please read this text about how to ask a good question. – José Carlos Santos May 11 '20 at 06:38
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    If there were 4 digits in the exponent also then you could say that the numbers are large. IIRC products of two natural numbers $<3000$ are handled precisely by modern pocket calculators, so I fail to see a problem here. Calculate the remainders of $1567^2$, square that to find the remainder of $1567^4$, multiply by $1567$. Done. – Jyrki Lahtonen May 11 '20 at 06:58

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Hint : You could start from $M \equiv (1567)^{5}$ mod $2881 \iff \begin{cases} M \equiv (1567)^{5} \mbox{mod} (43) \\ M \equiv (1567)^{5} \mbox{mod} (67)\end{cases}$

Try to reduce $1567$ mod $43$ and $67$, find a solution than combine them to get the solution mod $2881$.

jacopoburelli
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