- #1

math_grl

- 49

- 0

## Homework Statement

Show that [tex]{p \choose k} = \sum^{k+1}_{i=1} {p-i \choose p-k-1}[/tex] where [tex]\forall k < p \in \mathbb{Z}[/tex] and [tex]p[/tex] a prime.

## Homework Equations

This is part (b) to a problem. Part (a) is showing that [tex]1 + x + x^2 + \cdots + x^{p-1}[/tex] is irreducible in [tex]\mathbb{Q}[x][/tex].

## The Attempt at a Solution

I don't know how to apply part (a) to part (b)...Worked out the equality algebraically, then could probably do it by finite induction but think there has to be a shorter easier way that's supposed to follow from the previous part. Help.