more about Pythagorean triples

More about Pythagorean  triples

In  the Pythagorean triple (a,b,c) ,if all of them are even, it be a reducible set.  And if ‘a’ and ‘b’ are even ‘c’ will also be even. Hence In all the irreducible sets either ‘a’ or ‘b’ must  necessarily  be odd..All squares will have only certain number digits-1,4,7 and 9. .Since the sum of two squares  is equal to a square,the sum of number digits of a² and b² must be equal to the number digit of c². It requires that the number digit of either a² or b² must be 9 so that the number digit of the remaining square in one side will ne equal to the number digit of c². All numbers which are multiples of three will give number digit 9 for its square. Hence either ‘a’ or ‘b’ must be a multiple of three.If ‘a’ is multiple of three, then a² will be divisible by three.It means that c² – b² is divisible by three.that either (c-b) or (c+b) must be divisible by three.