In a Pythagorean triple there are three numbers: a, b and c and they are related to each other:

\Bigg \{ \begin{array}{ll} a < b < c \\ a^2 + b^2 = c^2 \end{array}

Represented in a Cartesian plane, a and b represent the two sides of a right-angled triangle while c is the hypotenuse.

Non-primitive Pythagorean triple

If a, b and c are coprime the triad is called primitive Pythagorean triple. Multiplying all three numbers by the same factor, we obtain a Pythagorean triplet, which takes the name of non-primitive Pythagorean triplet.

Generating a triple

Euclid’s formula is a fundamental formula for generating Pythagorean triples given an arbitrary pair of integers m and n with m > n > 0. The formula states that the integers

\Bigg \{ \begin{array}{ll} a = m^2-n^2 \\  b = 2mn \\  c = m^2+n^2 \end{array}

form a Pythagorean triple. a, b e c may form a non-primitive Pythagorean triple if m and n are not coprime and not both odd.

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