- In primenumbers@yahoogroups.com,

Kermit Rose <kermit@...> wrote:

> An integer z is a sum of two squares in exactly one way

This is clearly false. Simply consider 20 = 2^2 + 4^2.

> if and only if it is one of the following forms:

> (1) an odd power of 2, z = 2**(2*m+1) for m > 0

> (2) a prime equal to 1 mod 4

> (3) the square of a prime equal to 1 mod 4 or

> (4) z = p*h**2 where p is either 2, or an odd prime

> equal to 1 mod 4, or the square of an odd prime equal

> to 1 mod 4, and h has all prime factors equal to 3 mod 4.

David - I wrote:

> An odd number N is the sum of two coprime squares in precisely

and then "Kermit Rose" mistakenly claimed

> one way if and only if N is a prime congruent to 1 mod 4

> or a power of such a prime.

> David, a Minor correction is needed here

with the irrelevant observations

> 2**2 + 11**2 = 5**3

Note that 10^2 and 5^2 are not coprime.

> 10**2 + 5**2 = 5**3

David