Difference between revisions of "Perfect square"
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The sum of the first <math>n</math> square numbers (starting with <math>1</math>) is <math>\frac{n(n+1)(2n+1)}{6}</math> | The sum of the first <math>n</math> square numbers (starting with <math>1</math>) is <math>\frac{n(n+1)(2n+1)}{6}</math> | ||
| − | An integer <math>n</math> is a perfect square [[ | + | An integer <math>n</math> is a perfect square [[iff]] it is a [[quadratic residue]] [[modulo]] all but finitely [[prime]]s. |
== Perfect Square Trinomials == | == Perfect Square Trinomials == | ||
Latest revision as of 00:14, 29 November 2023
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 
.
See also
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