Pythagorean Triple Generator

How it is calculated

The tool applies Euclid's formula to two whole numbers m and n with m > n ≥ 1:

a = m² − n², b = 2mn, c = m² + n²

These always satisfy a² + b² = c², so they are the two legs and the hypotenuse of a right triangle with whole-number sides. Decimals are rejected, and so is any pair where m is not larger than n or n is below 1. The tool does not check that the triple is primitive. If m and n share a factor, or are both odd, the three numbers will have a common divisor (for m = 5 and n = 3 you get 16, 30, 34, which is 2 times 8, 15, 17).

Common mistakes

• Entering m smaller than or equal to n; the order matters, m must be the larger number.
• Typing decimals like 2.5, which are rejected. Both inputs must be whole numbers.
• Assuming every result is a primitive triple. Pairs such as 5 and 3 give 16, 30, 34, which reduces to 8, 15, 17.
• Expecting every triple to appear from a single pair. Euclid's formula gives primitive ones; non-primitive ones come from multiplying all three numbers by k, for example 6, 8, 10 from 3, 4, 5.
• Mixing up which number is the hypotenuse: c is always the largest, and a and b are the legs, though a may be larger or smaller than b.