# How Euler Secured The World

Leonhard Euler is defined as the father of mathematics. He lived from 1707 to 1783, and had a stunning research career, including contributions to mechanics, music and fluid dynamics. His shadow thus looms large over our modern world, including within cryptography.

One of his great theorems defined that:

aᴺ⁻¹≡1 (mod N)

The key factor here is that a and N should not share the same factors. We often define this as **gcd(a,N)=1**, and where gcd() is the greatest common denominator. If we use a few values of a and N we see [Try]: