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Sum of 3 Squares #2 (Posted on 2024-07-04)

The equation a² + b² + c² = d² has an infinite number of positive integer solutions.

(A) Prove that there are infinitely many solutions for which c is a multiple of a*b.

(B) Find a general formula that generates all such solutions.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Possible Solution

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Prove that there are infinitely many solutions for which c is a multiple of a*b

Let a=1, let b=2n, let c= 1*n*2n

then (1)^2+(2n)^2+(1)^2(n)^2(2n)^2 =(2n^2+1)^2

Always true.

Find a general formula that generates all such solutions.

The above formula generates all solutions of this form.

Posted by broll on 2024-07-05 00:11:49

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