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Re: Posting to Mma mailing list


>> So this equals  x^4 + a^4  if and only if  b^2 = 2 a^2 ,  that is
>> x^4 + n  factors over the integers if and only if  n = b^4 /4  for  b  an
>> integer
This might not be the ONLY way such a polynomial could factor. The result
is in fact due to Capelli:
Sulla riduttibilita della funzione $x^n-A$ in campo qualunque
di rationalit\`a.
Math. Ann. 54(1901) pp. 602-603.






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