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 equat
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] 