No 19

A Pythagorean Triple (a,b,c) is a set of three whole numbers which can form the sides of a right-angled triangle. So a² + b² = c².

You are familiar with the example (3,4,5) giving 3² + 4² = 5².

Multiples also work ... (6,8,10) and (9,12,15) etc.

Not so familiar is the fact that there are 18 triples (ignoring multiples) with the two smaller numbers less than 100. Here they are:

3 , 4 , 5	12 , 35 , 37	33 , 56 , 65
5 , 12 , 13	13 , 84 , 85	36 , 77 , 85
7 , 24 ,25	16 , 63 , 65	39 , 80 , 89
8 , 15 , 17	20 , 21, 29	48 , 55 , 73
9 , 40 , 41	20 , 99 , 101	60 , 91, 109
11 , 60 , 61	28 , 45 , 53	65 , 72 , 97

There are some remarkable patterns among these numbers. Can you find any?

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