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Need help on II-A Number theory 7.28

 
 
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Re: Need help on II-A Number theory 7.28
by Areteem Professor - Monday, April 19, 2021, 1:15 PM
 

Recall that the extension of Fermat's Little Theorem says that $a^{\phi(n)} \equiv 1 \pmod{n}$ if $\gcd(a,n) = 1$.

What can you say about $m^{\phi(n)} + n^{\phi(m)} \pmod{n}$ and $m^{\phi(n)} + n^{\phi(m)} \pmod{m}$?