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.

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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 ?