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An integer is square-free if and only if it is equal to its radical. Every positive integer can be represented in a unique way as the product of a powerful number (that is an integer such that is divisible by the square of every prime factor) and a square-free integer, which are coprime.
A non-negative integer is a square number when its square root is again an integer. For example, =, so 9 is a square number. A positive integer that has no square divisors except 1 is called square-free. For a non-negative integer n, the n th square number is n 2, with 0 2 = 0 being the zeroth one. The concept of square can be extended to some ...
In mathematics, a square-free element is an element r of a unique factorization domain R that is not divisible by a non-trivial square. This means that every s such that s 2 ∣ r {\displaystyle s^{2}\mid r} is a unit of R .
In mathematics, a square-difference-free set is a set of natural numbers, no two of which differ by a square number. Hillel Furstenberg and András Sárközy proved in the late 1970s the Furstenberg–Sárközy theorem of additive number theory showing that, in a certain sense, these sets cannot be very large.
Pages for logged out editors learn more. Contributions; Talk; Squarefree number
Ramanujan's constant is the transcendental number [5], which is an almost integer: [6] = … +. This number was discovered in 1859 by the mathematician Charles Hermite. [7] In a 1975 April Fool article in Scientific American magazine, [8] "Mathematical Games" columnist Martin Gardner made the hoax claim that the number was in fact an integer, and that the Indian mathematical genius Srinivasa ...
The radical of any integer is the largest square-free divisor of and so also described as the square-free kernel of . [2] There is no known polynomial-time algorithm for computing the square-free part of an integer.
For a nonzero square free integer , the discriminant of the quadratic field = is if is congruent to modulo , and otherwise . For example, if d {\displaystyle d} is − 1 {\displaystyle -1} , then K {\displaystyle K} is the field of Gaussian rationals and the discriminant is − 4 {\displaystyle -4} .