Euler S Theorem In Discrete Mathematics

Displaystyle varphi n is euler s totient function.

Euler s theorem in discrete mathematics. Http bit ly 1zbplvm subscribe on youtube. Phi n cdot k n 1. One thought on discrete math 2 euler s theorem susan hao says. In general euler s theorem states that if p and q are relatively prime then where φ is euler s totient function for integers.

That is is the number of non negative numbers that are less than q and relatively prime to q. When y e z is divided by z the remainder will always be 1 where e z is euler number of z and y and z are co prime to each other. In number theory euler s theorem also known as the fermat euler theorem or euler s totient theorem states that if n and a are coprime positive integers then a raised to the power of the totient of n is congruent to one modulo n or. We introduce euler s theorem in graph theory and prove it.

An euler circuit is an euler path which starts and stops at the same vertex. In my last post i explained the first proof of fermat s little theorem. When y e z k is divided by z where k is an integer remainder will always be 1 that is if the power is any multiple of the euler number of the divisor even in that case the remainder will be 1. Since ϕ n n 1 phi n le n 1 ϕ n n 1 we have n 1.

Solutions to 3 typical test questions. ϕ n k n 1. These elements are relatively co prime to q. Section 4 4 euler paths and circuits investigate.

Http bit ly 1vwirxw like us on fa. Since the set of numbers are relatively prime to q dividing by the term is permissible. Our goal is to find a quick way to check whether a graph or multigraph has an euler path or circuit. ϕ n k for some integer k k k.

By euler s theorem 2 ϕ n 1 m o d n 2 phi n equiv 1 pmod n 2 ϕ n 1 m o d n. June 26 2015 at 7 57 pm thank you so much for your videos. An euler path in a graph or multigraph is a walk through the graph which uses every edge exactly once. Remember that is the function that tells us how many positive integers less than are relatively prime to.