What is a benson rectangular number?

Answer 1

a positive integer A that, if increased or decreased by the same positive integer B, yields 2 positive integers, A+B and A-B, that are both perfect squares"

OK... i figured out kinda what it meant... i think the integer B is equal to A-1, like the rectangular number definition: n(n-1)

Answer 2

A Benson rectangular number is a positive integer that can be represented as the sum of two squares in more than one way. In other words, it can be expressed as a^2 + b^2 = c^2 + d^2, where a, b, c, and d are positive integers. These numbers are named after mathematician Karl D. Benson, who studied them extensively in the 1960s. Benson rectangular numbers have interesting properties and connections to number theory and Diophantine equations.

Answer 3

Well, sweetheart, a Benson rectangular number is a number that can be expressed as the sum of two consecutive squares. So, if you take the square of 5 (25) and the square of 6 (36) and add them together, you get 61, which is a Benson rectangular number. It's just a fancy way of saying math can be a little quirky sometimes.