perfect square is an element of algebraic structure that is equal to the square of another element. Square number, a perfect square integer. Perfect Square...

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with...

Perfect Square is a 2004 concert film of the alternative rock band R.E.M., filmed on July 19, 2003, at the Bowling Green in Wiesbaden, Germany. It was...

A most-perfect magic square of order n is a magic square containing the numbers 1 to n2 with two additional properties: Each 2 × 2 subsquare sums to 2s...

size of a square in the tiling. The order of a squared square is its number of constituent squares. A "perfect" squared square is a square such that each...

††† - Yen Press has the rights to series' digital release due to being a Square Enix title. 2001 Nights A, A Prime A.D. Police: Dead End City Abara Act-Age...

any field, where either –1, 2 or –2 is a square. In a finite field, the product of two non-squares is a square; this implies that the polynomial x 4 +...

other words, completing the square places a perfect square trinomial inside of a quadratic expression. Completing the square is used in solving quadratic...

a perfect power is a natural number that is a product of equal natural factors, or, in other words, an integer that can be expressed as a square or a...

allows the packing of n {\displaystyle n} unit squares is known when n {\displaystyle n} is a perfect square (in which case it is n {\displaystyle {\sqrt...

difference of two squares is a squared (multiplied by itself) number subtracted from another squared number. Every difference of squares may be factored...

S {\displaystyle S} . Since all square roots of natural numbers, other than of perfect squares, are irrational, square roots can usually only be computed...

of a perfect number (whether even or odd) must be even, because N cannot be a perfect square. From these two results it follows that every perfect number...

squaring.net. The lowest number of squares need for a perfect tiling of a rectangle is 9 and the lowest number needed for a perfect tilling a square is...

to squaring is quadratic. The square of an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often...

lemma can be used to show that two identical perfect squares can never be added to produce another perfect square. Suppose the contrary that 2 {\displaystyle...

the odd leg) are both perfect squares; however this is not a sufficient condition, as the numbers {1, 8, 9} pass the perfect squares test but are not a Pythagorean...

{\displaystyle 5x^{2}+4} or 5 x 2 − 4 {\displaystyle 5x^{2}-4} is a perfect square. This is because Binet's formula, which can be written as F n = ( φ...

{y}}} run forever on each input y {\displaystyle y} which is not a perfect square. Algorithms that compute ⌊ y ⌋ {\displaystyle \lfloor {\sqrt {y}}\rfloor...

one prime between consecutive perfect squares? Are there infinitely many primes p such that p − 1 is a perfect square? In other words: Are there infinitely...

has a pair of folded perfect squares, one on each side of the equation. The two perfect squares balance each other. If two squares are equal, then the...

to just check if 24x + 1 is a perfect square. For non-generalized pentagonal numbers, in addition to the perfect square test, it is also required to check...

the square root of numbers having many digits. It was known to the ancient Greeks that square roots of positive integers that are not perfect squares are...

integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e., if there exists an integer x such that: x 2 ≡ q ( mod...

\end{aligned}}} Because the left-hand side is now a perfect square, we can easily take the square root of both sides: x + b 2 a = ± b 2 − 4 a c 2 a ....

with perfect square sides are related to the Perfect cuboid problem. As of February 2021, only two primitive Heronian triangles with perfect square sides...

of squares. Except for n ≤ 5, the enumeration of higher order magic squares is still an open challenge. The enumeration of most-perfect magic squares of...

neighboring site by Abbot Richbold (784–804) the cloister was made a perfect square, against the south flank of the new church, precisely as in the plan...

For instance, to estimate the square root of 15, one could start with the knowledge that the nearest perfect square is 16 (42). root ≃ 4 − 16 − 15 2...

is thought that there are more positive integers than perfect squares, since every perfect square is already positive, and many other positive integers...