On Pythagorean triangles - Schinzel, Andrzej (Annales Mathematicae Silesianae, 1998)
The following theorem answers a question asked by I. Korec at the Second Czech & Polish Conference on Number Theory. Theorem. If m∈ℕ, ord2m is even, x0,y0,z0∈ℤ and (1) x02+y02 ≡ z02(modm), then there exist x,y,z∈ℤ such that x2+y2 = z2, x2 ≡ x02, y2 ≡ y02, z2 ≡ z02(modm).