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## Main Question or Discussion Point

I've got a pair of (related) problems that are keeping me stumped. The two problems they are asking me to prove are:

[tex] p^{(q-1)} + q^{(p - 1)} \equiv 1 \; (\!\!\!\!\!\! \mod \, pq) [/tex]

[tex]a^{\phi(b)} + b^{\phi(a)} \equiv 1

\; (\!\!\!\!\!\! \mod \, ab)[/tex]

Where [tex] \phi(n) [/tex] is Euler's Totient Function.

I know that these are similar, as the second problem is using Euler's Theorem, a generalization of Fermat's Little Theorem, I just can't seem to figure them out.

[tex] p^{(q-1)} + q^{(p - 1)} \equiv 1 \; (\!\!\!\!\!\! \mod \, pq) [/tex]

[tex]a^{\phi(b)} + b^{\phi(a)} \equiv 1

\; (\!\!\!\!\!\! \mod \, ab)[/tex]

Where [tex] \phi(n) [/tex] is Euler's Totient Function.

I know that these are similar, as the second problem is using Euler's Theorem, a generalization of Fermat's Little Theorem, I just can't seem to figure them out.