perfectsquare is an element of algebraic structure that is equal to the square of another element. Square number, a perfectsquare integer. Perfect Square...
In mathematics, a square number or perfectsquare is an integer that is the square of an integer; in other words, it is the product of some integer with...
PerfectSquare 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...
size of a square in the tiling. The order of a squaredsquare is its number of constituent squares. A "perfect" squaredsquare is a square such that each...
difference of two squares is a squared (multiplied by itself) number subtracted from another squared number. Every difference of squares may be factored...
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 perfectsquare trinomial inside of a quadratic expression. Completing the square is used in solving quadratic...
of a perfect number (whether even or odd) must be even, because N cannot be a perfectsquare. From these two results it follows that every perfect number...
††† - 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...
S {\displaystyle S} . Since all square roots of natural numbers, other than of perfectsquares, are irrational, square roots can usually only be computed...
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...
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...
lemma can be used to show that two identical perfectsquares can never be added to produce another perfectsquare. Suppose the contrary that 2 {\displaystyle...
the odd leg) are both perfectsquares; however this is not a sufficient condition, as the numbers {1, 8, 9} pass the perfectsquares test but are not a Pythagorean...
{\displaystyle 5x^{2}+4} or 5 x 2 − 4 {\displaystyle 5x^{2}-4} is a perfectsquare. 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 perfectsquare. Algorithms that compute ⌊ y ⌋ {\displaystyle \lfloor {\sqrt {y}}\rfloor...
has a pair of folded perfectsquares, one on each side of the equation. The two perfectsquares balance each other. If two squares are equal, then the...
to just check if 24x + 1 is a perfectsquare. For non-generalized pentagonal numbers, in addition to the perfectsquare test, it is also required to check...
integer q is called a quadratic residue modulo n if it is congruent to a perfectsquare modulo n; i.e., if there exists an integer x such that: x 2 ≡ q ( mod...
the square root of numbers having many digits. It was known to the ancient Greeks that square roots of positive integers that are not perfectsquares are...
\end{aligned}}} Because the left-hand side is now a perfectsquare, we can easily take the square root of both sides: x + b 2 a = ± b 2 − 4 a c 2 a ....
allows the packing of n {\displaystyle n} unit squares is known when n {\displaystyle n} is a perfectsquare (in which case it is n {\displaystyle {\sqrt...
with perfectsquare sides are related to the Perfect cuboid problem. As of February 2021, only two primitive Heronian triangles with perfectsquare sides...
neighboring site by Abbot Richbold (784–804) the cloister was made a perfectsquare, against the south flank of the new church, precisely as in the plan...
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...
divides a2 + b2. Prove that a2 + b2/ab + 1 is a perfectsquare. Fix some value k that is a non-square positive integer. Assume there exist positive integers...
in this case, n+1 = (p+1)2 is a perfectsquare. One can quickly detect perfectsquares using Newton's method for square roots. By combining a Lucas pseudoprime...
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