3 Jul
2006
3 Jul
'06
12:14 p.m.
RKG wrote:
Presumably 0! = 1! = 0^2 + 1^2. 2! = 1^2 + 1^2 6! = 12^2 + 24^2
are the only integer solutions of
n! = x^2 + y^2
but is there a proof? R.
A number n can be written as a sum of two squares if and only if every prime congruent to 3 mod 4 appears in n's prime factorization with an even exponent. And Erdos proved the following refinement of Bertrand's postulate: the interval from n to 2n always contains both a 1 mod 4 and a 3 mod 4 prime. That'll do it. --Michael Kleber -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.