According to the Brahmagupta identity, the set of sums of one of these numbers and an integral multiple of another is closed under multiplication.
According to the Brahmagupta identity, the set of sums of one of these numbers and an integral multiple of another is closed under multiplication. The n equals two case of a class of Diophantine equations named for Pell in these numbers yields a hyperbola. Fermat proved that a prime number congruent to 1 modulo 4 can be written as the sum of two of these numbers. Adding two successive triangular numbers yields one of these numbers, and the sum of the first n of these is equal to n times n plus one times two n plus one over 6. Ending only in 0, 1, 4, 5, 6, and 9 for base-10 integers and including 1, 4, 9, and 16, for 10 points, name these products of a number with itself. 
According to the Brahmagupta identity, the set of sums of one of these numbers and an integral multiple of another is closed under multiplication.
square numbers [accept perfect squares] 