@Payel: Fermat's theorem on the sum of two squares applies. It says that an
odd prime p can be written as the sum of two perfect squares if and only if
p is congruent to 1 (mod 4). See
http://en.wikipedia.org/wiki/Proofs_of_Fermat's_theorem_on_sums_of_two_squares.
Thus, since 29 is congruent to 1 (mod 4), it can be written as the sum of
two squares, as you have demonstrated. But, e.g., 7, 11, and 19 cannot be
written as the sum of two perfect squares.
Code follows:
int PrimeIsSumOfTwoSquares(int p)
{
return (p & 3) == 1;
}
Dave
On Saturday, June 2, 2012 2:31:43 PM UTC-5, payel roy wrote:
> How do you verify whether sides of rectangular area are integer number If
> square of diagonal of a rectangular area is prime?
>
> Ex : Let's say square of a diagonal is : 2
>
> 2 = 1^2 + 1^2 [where 1,1 are the sides of the rectangular area]
>
> square of a diagonal is : 29
>
> 29 = 5^2 + 2^2.
>
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