Two consecutive triangular numbers sum to one of these numbers.
The sum of four of these numbers can represent any natural number according to a theorem of Lagrange. A formula that gives the sum of successive numbers of this type from zero to N is N times the quantity N plus one times the quantity two N plus 1, all divided by six. The product of two consecutive odd numbers is one less than one of these numbers. Two consecutive triangular numbers sum to one of these numbers. For 10 points, multiplying any integer with itself yields what type of non-prime number, such as four, nine, and sixteen?
The sum of four of these numbers can represent any natural number according to a theorem of Lagrange.
square numbers [or perfect squares]