Perfect square: Difference between revisions
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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> | ||
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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