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In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a superscript 2; for instance, the square of 3 may be written as 3 2, which is the number 9.
For example, 9 is a square number, since it equals 3 2 and can be written as 3 × 3. The usual notation for the square of a number n is not the product n × n, but the equivalent exponentiation n 2, usually pronounced as "n squared". The name square number comes from the name of the shape.
Likewise, tan 3 π / 16 , tan 7 π / 16 , tan 11 π / 16 , and tan 15 π / 16 satisfy the irreducible polynomial x 4 − 4x 3 − 6x 2 + 4x + 1 = 0, and so are conjugate algebraic integers. This is the equivalent of angles which, when measured in degrees, have rational numbers. [2] Some but not all irrational ...
Nine is the third square number (3 2), and the second non-unitary square prime of the form p 2, and, the first that is odd, with all subsequent squares of this form odd as well. Nine has the even aliquot sum of 4, and with a composite number sequence of two (9, 4, 3, 1, 0) within the 3-aliquot tree.
y = x 3 for values of 1 ≤ x ≤ 25.. In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 2 3 = 8 or (x + 1) 3.
The expression b 2 = b · b is called "the square of b" or "b squared", because the area of a square with side-length b is b 2. (It is true that it could also be called "b to the second power", but "the square of b" and "b squared" are more traditional)
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Gauss [10] pointed out that the four squares theorem follows easily from the fact that any positive integer that is 1 or 2 mod 4 is a sum of 3 squares, because any positive integer not divisible by 4 can be reduced to this form by subtracting 0 or 1 from it. However, proving the three-square theorem is considerably more difficult than a direct ...