**Cool Thing About Pythagorean Triplets**

There is a cool property of all odd numbers except one, they can all form Pythagorean triplets. A Pythagorean triplet is any set of positive integers a, b, and c that satisfy the equation a^{2 }+ b^{2 }= c^{2}. For example, a= 3, b= 4, and c= 5 is a Pythagorean triplet because 3^{2 }+ 4^{2 }= 5^{2}. If a is any odd number except 1, it can make a Pythagorean Triplet of the form a= a, b= (a^{2 }– 1)/2, and c= (a^{2} – 1)/2 + 1, or b + 1. You can prove this by substituting b and c with b= (a^{2} – 1)/2 and c= (a^{2} – 1)/2 + 1 in the equation a^{2 }+ b^{2 }= c^{2}. “a” cannot be even for this case because if a were even, (a^{2 }-1)/2 would not be a whole number, and a cannot be one, because then, b would be zero. For all other odd numbers, this would work, and Pythagorean Triplets of this form include…

a= 5, b= 12, c= 13

a= 7, b= 24, c= 25

a= 9, b= 40, c= 41