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Euler's Totient Theorem Problem 1 Solution

Revision as of 14:23, 23 April 2021 by Borealbear (talk | contribs) (Created page with "==Problem== (BorealBear) Find the last two digits of <math> 7^{81}-3^{81} </math>. ==Solution== This is a direct application of Euler's Totient Theorem. Since <math> \phi(10...")
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Problem

(BorealBear) Find the last two digits of $7^{81}-3^{81}$.

Solution

This is a direct application of Euler's Totient Theorem. Since $\phi(100)=40$, this reduces to $7^1-3^1\equiv \boxed{04}\pmod{100}$.

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