Incomplete question. conditions do not make sense.

akdayal wrote:Incomplete question. conditions do not make sense.

Really sorry for that. Correction done.

If a and b are both positive integers, is (b^(a+1))-(b*a^b) odd?

1. a+(a+4)+(a-8)+(a+6)+(a-10) is odd
2. (b^3)+3(b^2)+5b+7 is odd

take st1: a + (a +4) + (a -8) + (a + 6) + ( a-10) is odd
==> 5a -8 == odd
==> odd - even = odd ==> a is odd

Now main question
b(b^a - a^b) ------------ (1)
lets say if b is even +ve then clearly (1) will be even.
lets say b is odd then (1) becomes like
odd (odd^odd - odd^odd) ==> odd*(odd -odd) ==> odd *even ==> even
hence even

So statement 1 alone is suff

Now st2 is also suff as you have already mentioned that it is clear.
basically if you expand st2 you will get b is even

Hope this will help you