Square triangular number
In mathematics, a square triangular number (or triangular square number) is a number which is both a triangular number and a square number, in other words, the sum of all integers from 1 {\displaystyle 1} to n {\displaystyle n} has a square root that is an integer. There are infinitely many square triangular numbers; the first few are: == Solution as a Pell equation == Write N k {\displaystyle N_{k}} for the k {\displaystyle k} th square triangular number, and write s k {\displaystyle s_{k}} and t k {\displaystyle t_{k}} for the sides of the corresponding square and triangle, so that Define the triangular root of a triangular number N = n ( n + 1 ) 2 {\displaystyle N={\tfrac {n(n+1)}{2}}} to be n {\displaystyle n} .