The difference of two of these numbers can be factored into the sum and difference of two numbers, a and b.
For two primes p and q, one of these numbers is congruent to q mod p and congruent to p mod q unless both p and q are congruent to three mod four, according to Gauss's reciprocity theorem. A prime congruent to one mod four can be written as a unique sum of two of these numbers, as stated by Fermat. These numbers can be expressed as the sum of two consecutive triangular numbers. This type of number gives an integer when exponentiated to the one-half power. The difference of two of these numbers can be factored into the sum and difference of two numbers, a and b. For 10 points, identify these numbers that are the products of multiplying an integer by itself.
For two primes p and q, one of these numbers is congruent to q mod p and congruent to p mod q unless both p and q are congruent to three mod four, according to Gauss's reciprocity theorem.
perfect squares [or square numbers] &lt;CV&gt;