So I revising Binomials until I came across this question...
i) Given that $a=y+d $ use the binomial expansion of $(y+d)^{n},$ where $n$ is positive integer, to show that $a^{n}-y^{n-1}(y+nd) $ is divisible by $d^{2}$
ii) Hence show that if $a$ is the first term, $d$ the common difference, $L$ the $n$-th term of an arithmetic progression, then $a^{n}-L(a-d)^{n-1}$ is divisible by $d^{2}$
I could do the first part but I am stuck on the next....
Hint: $a-d=y$, $L = a + (n-1)d = y+nd$.