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: If <math>a</math> is odd, then <math>b=\frac{a^2}{2}-\frac{1}{2}</math> and <math>c=b+1</math>
: If <math>a</math> is odd, then <math>b=\frac{a^2}{2}-\frac{1}{2}</math> and <math>c=b+1</math>
: If <math>a</math> is even, then <math>b=\frac{a^2}{4}-1</math> and <math>c=b+2</math>
: If <math>a</math> is even, then <math>b=\frac{a^2}{4}-1</math> and <math>c=b+2</math>
[[Euclid]]'s formula is a fundamental formula for generating all possible Pythagorean triples given an arbitrary pair of integers <math>m</math> and <math>n</math> with <math>m>n>0</math>. The formula states that the following integers form a Pythagorean triple:
:<math> a=m^2-n^2,\ \,b=2mn,\ \,c=m^2+n^2</math>
There are many other formulas for generating such triples.
==Notes==
==Notes==
{{reflist}}
{{reflist}}
[[Category:Mathematics]]
[[Category:Mathematics]]