Recent content by qamaz

What is the meaning of $$\mathbb{Z}^{n}$$?

$$\text{ Let } n∈ \mathbb{N} \text{ and } S_{n} \text{ symmetrical group on } \underline n\underline . \text{ Let } π ∈ S_{n} \text{ and z } \text{ the number of disjunctive Cycles of π. Here will be counted 1 - Cycle }. (a) \text{ Prove that } sgn (π) = (-1)^{n-z}. (b) \text{ Prove that...

$$\text{ Let } n∈N \text{ and } (a1,a2,…,a_{n})∈\mathbb{Z}^{n}. \text{ Prove that always exist } i,j∈ \underline{n} \text{ with } i≤j \text{ so } \sum\limits_{k=i}^{\\j} a_{k} \text{ divisible by n} .$$