A strong equation?

Question

a^(n)-b^(n) = (a-b)^(n)+nk(a-b)
here if either "a" or "b" is odd and "n" is any prime & 4 then "k" will be a rational number.
prove that it is impossible to write
(a-b)^(n)+nk(a-b) =1
for n>2.
if n=2 then a & b will have infinite solutions for certain k`s
for e.g
if n=2 take k=0.75 then a=1.25 & b=0.75.

Answer 1

I think this thing can be easily proved with the help of mathematical induction. Start reverse of it, that is if we can write (a-b)^n+nk(a-b)=1, it means 'k' is not a rational number. So start with n>2 and 'k' comes out to be a rational number which contradicts our assumption. Hence, the thing is impossible to write.

Answer 2

I already answered this question.
The exampe you are giving is not correct :
b neither a is odd in your question.

You better think before you ask something.

http://answers.yahoo.com/question/index?qid=20061026224936AAq3sJN&r=w#TcN9CzS6VzONhsq.wd.QuxWnGugfyI_J1Sop2vP9e9hWrJbAbDeo