re:-modified laws of numbers.?

Question

any given number with any given power can be expressed as difference of at least one set of two perfect squares.what happens when the power is 1?

since the number 2 cannot be expressed as difference of two integer perfect squares so any number having a single 2 as its multiple like 6,10 14 cannot be expressed as difference of two integer perfect squares.

Answer 1

I don't know where this law of numbers came from....

But...

Maybe what it should say is..."Any odd number with any given power can be expressed as a difference of one consecutive set of two perfect squares."...since that statement is true...

The difference between two consecutive squares is, in fact, the sequence of odd numbers.

This is interesting too, because all prime numbers will be included in this sequence, except for 2.

Answer 2

Can you better formulate this problem in another way.The power is always integer, i guess otherwise it cant be expressed.but my answer would be its not difficult to express:
let X be number.Then X = a^2 - b^2 = (a+b)(a-b)
now we can choose the value such that this happens..