Question

Let n be a natural number, and M = 5^n. If E = 3^M and E + 1 is divided by 7, then the remainder is ..

Answer 1

First, write it as \[\Large 3^{5^n}+1\pmod7\]This means we want to find \[\Large e^{5^n}\pmod7\]

Answer 2

That should be 3 instead of an e at the end.

Answer 3

Hence, we need to find \[5^n\pmod6\]Can you tell me what this will be?

Answer 4

Hint: Rewrite 5 as another number mod 6. Your solution should depend on whether \(n\) is even or odd.