An integer is said to be a perfect square if there is an integer so that . The first few perfect squares are .
The sum of the first square numbers (starting with ) is
An integer is a perfect square iff it is a quadratic residue modulo all but finitely primes.
Perfect Square Trinomials
A type of perfect square is an equation that is a perfect square trinomial. For example, .
Perfect square trinomials are a type of quadratic equation that have terms and contain unique root.
For any quadratic equation in the form , it is a perfect square trinomial iff .
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