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  2. Square-free integer - Wikipedia

    en.wikipedia.org/wiki/Square-free_integer

    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.

  3. Square-free element - Wikipedia

    en.wikipedia.org/wiki/Square-free_element

    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 .

  4. Congruent number - Wikipedia

    en.wikipedia.org/wiki/Congruent_number

    However, in the form that every congruum (the difference between consecutive elements in an arithmetic progression of three squares) is non-square, it was already known (without proof) to Fibonacci. [4] Every congruum is a congruent number, and every congruent number is a product of a congruum and the square of a rational number. [5]

  5. Quadratic field - Wikipedia

    en.wikipedia.org/wiki/Quadratic_field

    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} .

  6. Radical of an integer - Wikipedia

    en.wikipedia.org/wiki/Radical_of_an_integer

    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.

  7. Square number - Wikipedia

    en.wikipedia.org/wiki/Square_number

    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 ...

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