Pythagorean Triples

October 26, 2012

Today’s exercise feels like a Project Euler problem:

A pythagorean triple consists of three positive integers a, b and c with a < b < c such that a2 + b2 = c2. For example, the three numbers 3, 4 and 5 form a pythagorean triple because 32 + 42 = 9 + 16 = 25 = 52.

The perimeter of a pythagorean triple is the sum of the three numbers that make up the pythagorean triple. For example, the perimeter of the 3, 4, 5 pythagorean triple is 3 + 4 + 5 = 12. There are 17 pythagorean triples with perimeter not exceeding 100. Ordered by ascending perimeter, they are: 3, 4, 5; 6, 8, 10; 5, 12, 13; 9, 12, 15; 8, 15, 17; 12, 16, 20; 7, 24, 25; 15, 20, 25; 10, 24, 26; 20, 21, 29; 18, 24, 30; 16, 30, 34; 21, 28, 35; 12, 35, 37; 15, 36, 39; 9, 40, 41; and 24, 32, 40.

How many pythagorean triples exist with perimeter not exceeding one million?

Your task is to write a program to compute the count of pythagorean triples with perimeter not exceeding one million. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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