# Math11U

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A Pythagorean Triple is a set of integers that satisfy the Pythagorean Theorem, c squared= a squared + b squared. 3,4,5 and 5,12,13 are just two of many examples. Find another, that is not a multiple of the one of the two given, using the following formula.

n squared- m squared,2mn, n squared+ m squared, where m,n E I and n>m

• Math11U -

n^2-m^2, 2mn , n^2 + m^2 , where n > m will always produce a Pythagorean triple.

If n and m are also relatively prime, that is they have no common factor between them, then that triple will also be unique.

e.g. n= 12, m=7

12^2-7^2 = 144 - 49 = 95
2(12)(7) = 168
12^2 + 7^2 = 144 + 49 = 193

95, 168, and 193 are a PT , and are not a multiple of any other PT.

• Math11U -

Just a question.. should I have 3 numbers and not only two?

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