MathDB

retriangular and triangular numbers , aT +b

Source: 2020 Colombia day 1 p3

November 27, 2022

number theoryTriangular number

Problem Statement

A number is said to be triangular if it can be expressed in the form

1 + 2 +...+n

for some positive integer

n

. We call a positive integer

a

retriangular if there exists a fixed positive integer

b

such that

aT +b

is a triangular number whenever

T

is a triangular number. Determine all retriangular numbers.