# Difference between revisions of "Perfect square"

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The sum of the first <math>n</math> square numbers (not including 0) is <math>\frac{n(n+1)(2n+1)}{6}</math> | The sum of the first <math>n</math> square numbers (not including 0) is <math>\frac{n(n+1)(2n+1)}{6}</math> | ||

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+ | An integer <math>n</math> is a perfect square iff it is a [[quadratic residue]] [[modulo]] all but finitely primes. | ||

== Perfect Square Trinomials == | == Perfect Square Trinomials == |

## Revision as of 13:39, 27 September 2007

An integer is said to be a **perfect square** if there is an integer so that . The first few perfect squares are 0, 1, 4, 9, 16, 25, 36.

The sum of the first square numbers (not including 0) is

An integer is a perfect square iff it is a quadratic residue modulo all but finitely primes.

## Perfect Square Trinomials

Another type of perfect square is an equation that is a perfect square trinomial. Take for example

.

Perfect square trinomials are a type of quadratic equation that have 3 terms and contain 1 unique root.

For any quadratic equation in the form , it is a perfect square trinomial iff .

## See also

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