Suppose that are integers, none of which is divisible by .
Show that . Hint: work modulo .
I can only think of these congruences by Fermat's Little Theorem.
How can I get congruences in modulo 25 and prove the statement?
Is it proved by assuming that and then show a contradiction like the proof for in
https://en.wikipedia.org/wiki/Proof_of_Fermat's_Last_Theorem_for_specific_expone nts ?