modified law of numbers.?

Question

any given number except 1 can be expressed as difference of sets of two perfect squares at least once.what happens when a power is added to that number?

read what happens when a power is given to that number.

Answer 1

Assume we found an integer N where N = x^2 - y^2 where a and b are integers.

can N^k be expressed in such a form too? Is that what u r asking?

Only N that can be factored as N=c.d where c and d are both odd, or even, can be expressed as N = x^2 - y^2 for integer x and y.

So, if N=c.d where c and d r both odds(or even), N^k=c^k.d^k.... and since odd^k is still odd and even^k is still even, N^2 can be expressed as x^2 - y^2 for some integers x and y.