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I could use two loops to check for all combinations of two integers that less than p prime, but it’s very inefficient. Is there a better algorithm to approach this problem? Any idea?
Where p mod 4 = 1.
Thanks,
You can try using the Hermite-Serret algorithm.
You can also find a good list of algorithms on this math.se page: https://math.stackexchange.com/questions/5877/efficiently-finding-two-squares-which-sum-to-a-prime
See especially, Robin Chapman’s answer: https://math.stackexchange.com/questions/5877/efficiently-finding-two-squares-which-sum-to-a-prime/5883#5883