Pronic number/Extensions

Math

This page is meant to be a page for how pronic numbers can be generalized.

How it can be generalized
Every positive integer is Pronic(n), where n can be any number.

Formula
We need \(n^2+n=y\), where y is the number being a 'generalized pronic number'.

We will get \(n^2+n+(-y)=0\).

Using the quadratic formula,

\[n=\frac{-1\pm\sqrt{1+4y}}{2}\]

Note the signs between 1 and 4y.