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Pythagorean number law (any three numbers can meet the conditions of Pythagorean theorem)

2022-07-04 19:36:00 【Acacia moon tower】

One 、 Number of Pythagorean shares

Form like $a^{2}+b^{2} = c^{2}$ One The number of classes is called Pythagorean number （a,b,c As a positive integer ）.

Two 、 Some properties

1. The two right sides and hypotenuse of a right triangle satisfy the Pythagorean number theorem .

2. a+b>c . a-b<c .

3. When a In an odd number of , a=2n+1 , be $b=2n^{2}+2n$ , $c=2n^{2}+2n+1$ . $n\in \left \{ 1,2,3,4.......\right \}$

4. When a For even when , a=2n+2 , be $b=n^{2}+2n$ , $c=n^{2}+2n+2$ . $n\in \left \{ 1,2,3,4.......\right \}$

3、 ... and 、 Fermat's theorem

$a^{n}+b^{n}=c^{n}$ , When n>2 when , The equation has no positive solution .

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