can u give an example?

Question

a^(n)-b^(n)
=(a-b)^(n)+nk(a-b)
here when "a" is an odd natural number , "b" is any natural number other then "a" and "n" is any prime number or its factors are the same prime (the numbers whose multiples are 5 like 25 ,125 etc are excluded but the case of 5 is included.) then "k"will always be a natural number.
give an example to prove it wrong.

Answer 1

This does not have any counter example as this is mathemetically correct.
to prove it let a = (b+c)

a^n - b^n
= (c+b)^n - b^n
using bionomial theorerm
the 1st is sum of n+1 terms kth term is
n
C c^k*b^(n-k)
K
when k =n the last term = b^n which cancells

ther 1st term = c^n
all other terms are multiple of n and c so can be added to give your expression by choosing suitable K

so it is true for all cases for suitable k

Answer 2

no there is no example that it is wrong.

any expression with natural numbers that only uses the operator + - * ^ results in a natural number.

So if you have equality then K has to be a natural number, sinse the lft side is a natural number.

Answer 3

me no understand ur question