## Re: Formula

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• In primenumbers@yahoogroups.com, ... This is clearly false. Simply consider 20 = 2^2 + 4^2. David
Message 1 of 11 , Oct 4 10:01 AM
Kermit Rose <kermit@...> wrote:

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

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

David
• ... and then Kermit Rose mistakenly claimed ... with the irrelevant observations ... Note that 10^2 and 5^2 are not coprime. David
Message 2 of 11 , Oct 4 10:13 AM
I wrote:

> An odd number N is the sum of two coprime squares in precisely
> one way if and only if N is a prime congruent to 1 mod 4
> or a power of such a prime.

and then "Kermit Rose" mistakenly claimed

> David, a Minor correction is needed here

with the irrelevant observations

> 2**2 + 11**2 = 5**3
> 10**2 + 5**2 = 5**3

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

David
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