(a^m^2 + 1) | (a^n^2 - 1) ???
I'm sure there is a quick trick I'm missing somewhere... but anyone have any ideas on how to prove:
(a^m^2 + 1) | (a^n^2 - 1) , for n > m.
[Show [a^(n^2) -1] is divisible by [a^(m^2) +1]
Thanks a lot. . .
(I've tried letting k=n-m, and other stuff like that... kept going in circles. I'm guessing Fermat's Little Thm comes in somewhere?)
It's not true. A counterexample exists among the very small integers...
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