Question

please prove the theorems, thank you very much

8.21 Theorem. A natural numbern can be written as a sum of two squares of natural numbers if and only if every prime congruent to 3 modulo 4 in the unique prime factorization of n occurs to an even power Pythagorean triples revisited We are now in a position to describe the possible values for the hypotenuse in a primitive Pythagorean triple. 8.22 Theorem. If (a, h, e) is a primitive Pythagorean triple, then c is a product of primes each of which is congruent to 1 modulo 4 8.23 Theorem. f the natural mumber c is a product of primes each of which is congruent to I modulo 4, then there exist integers a and b such that (a, b, e) is a primitive Pythaygorean triple.

Answer 1

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