Give two example of pythagorean triplet
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Most elementary number theory texts prove that all primitive triples (a,b,c) are given by the following:
a = u2 - v2, b = 2uv, c = u2 + v2
where u and v are relatively prime integers, not both odd. Notice that a is a difference of squares, so for it to be prime we need that u and v differ by 1. So
a = 2v + 1, b = 2v2 + 2v, and c = 2v2 + 2v + 1.
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, (3, 4, 5) and (5, 12, 13) are examples of primitive Pythagorean triples because each set has a common factor of 1 and also satisfies thePythagorean theorem: a2 + b2 = c2.
(3, 4, 5) → GCF =1
a2 + b2 = c232 + 42 = 52
9 + 16 = 25
25 = 25
(5, 12, 13) → GCF = 1
a2 + b2 = c2
52 + 122 = 132
25 + 144 = 169
169 = 169
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