On Pythagorean triangles
Abstract
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).
Keywords
Pythagorean triangles
Instytut Matematyczny Polskiej Akademii Nauk Poland
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