Question

the the three natural numbers 5, 12, 13 are in Pythagorean triplets or not if yes then prove it​

Answer 1

Yes it is.

5^2 + 12^2 = 25 + 144 = 169 = 13^2

It is also a primitive Pythagorean triple since 5, 12 and 13 have no common divisor larger than 1.

All Pyhagorean triplets can be found by Euclid’s formula

given an arbitrary pair of integers m and n with m > n > 0. The formula states that the integers

a = m^2 - n^2, b = 2mn, c = m^2 + n^2 are Pythagorean triplets.

For m=3, n=2 gives a = 9–4=5 b=2x3x2=12 and c=9+4=13 a Pythagorean triplet

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