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et P be an odd prime number. Suppose there are two natural numbers A, B such...

  1. et P be an odd prime number. Suppose there are two natural numbers A, B such that 2P = A2 + B2.
  1. Show that A, B are odd and coprime.
  2. Show that P ≡ 1 (mod 4).
  3. Write P as a sum of two squares of natural numbers.
  4. Find a Primitive Pythagorean Triple (U, V, P).
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