https://www.tandfonline.com/doi/abs/10.1080/00207390050032351#:~:text=Euler%20generalized%20Fermat’s%20Theorem%20in,modn)is%20not%20always%20valid.
Euler generalized Fermat’s Theorem in the following way: if gcd (x,n) = 1 then xφ(n) ≡ 1(modn), where φ is the Euler phi-function. It is clear that Euler’s result cannot be extended to all integers x in the same way Fermat’s Theorem can; that is, the congruence xφ(n)+1 ≡ x(modn)is not always valid.
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