fermat aware of euler's result i've added reference k ek luca somer p remark to the claim that fermat probably knew this result however the claim that it is widely believed might be too strong the mentioned remarks says the following remark as mentioned in the literature cf e g lenstra lenstra manasse pollard fermat probably knew the previous theorem although its proof was given later by euler in see burton p however it is then unclear why fermat did not apply this theorem to the factorization of f it was sufficient to divide f only by primes of the form k and for k fermat could have convinced himself that his hypothesis on the primality of fm did not hold concerning the factor of f see figure we note that there are primes of the form k for k