How can i solve this pythagorean triplet problem?

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I came across this pythagorean triplet problem. According to which there is exactly one pythagorean triplet for which

a+b+c = 1000

Pythagorean Triplet: a set of three natural numbers, a smaller than b smaller than c, for which,

a^2 + b^2 = c^2

for example:

3^2 + 4^2 = 9 + 16 = 25 = 5^2

P.S: I don't need exact solution, I just need some hint because I didn't find the triplet. Either it is smaller than 1000 or greater but not equal.