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May 19, 2015 at 13:35 comment added Linus Hamilton True enough. :) This is the only solution with $p<10^8$. The case $a=2$ should boil down to a Pell-like equation. But I don't want to dig too deep into it without hearing OP's response, as I don't know how (313, 181) and their possible friends apply to finite groups.
May 19, 2015 at 13:32 comment added LSpice "I said nontrivial." (mathoverflow.net/q/27305/2383)
May 19, 2015 at 13:27 history answered Linus Hamilton CC BY-SA 3.0