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**mathguy80** Hi Guys,

Need a little help with this one, Not sure how to proceed.

Two positive integers, $\displaystyle a,b$ are connected by the relation $\displaystyle a = b - 1$. By using a binomial expansion show that for all positive integral values of n the expression $\displaystyle a^{2n} + 2nb - 1$ is exactly divisible by $\displaystyle b^2$. By choosing suitable values of a and n, show that $\displaystyle 2^{40} + 119$ is divisible by 9, and hence that $\displaystyle 2^{39} + 1$ is divisible by 9.

I tried putting the substitution for $\displaystyle a$ into the equation, and did a binomial expansion of $\displaystyle (b - 1)^{2n}$, but not sure where that is supposed to lead. It seems like another longer equation.

Thanks for your help.