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How can I transform the product 365(15^2+16^2) into sum of two squares???

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  • $\begingroup$ There are sixty-four different integer solutions to $x^2+y^2=365(15^2+16^2)$... are you looking for any particular solution or all of them? $\endgroup$ – JMoravitz Nov 22 '16 at 7:48
  • $\begingroup$ Any of them. I need the method. $\endgroup$ – Avirup Biswas Nov 22 '16 at 7:50
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See How do you prove that a prime is the sum of two squares iff it is congruent to 1 mod 4?

As $365=5\cdot73$

$5=1^2+2^2$

$73=8^2+3^2$

Use Brahmagupta-Fibonacci Identity $$(a^2+b^2)(c^2+d^2)=(ac\pm bd)^2+(ad\mp bc)^2$$

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