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  2. Fermat's factorization method - Wikipedia

    en.wikipedia.org/wiki/Fermat's_factorization_method

    Fermat's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares: N = a 2 − b 2 . {\displaystyle N=a^{2}-b^{2}.} That difference is algebraically factorable as ( a + b ) ( a − b ) {\displaystyle (a+b)(a-b)} ; if neither factor equals one, it is a proper ...

  3. Fermat number - Wikipedia

    en.wikipedia.org/wiki/Fermat_number

    The Fermat numbers satisfy the following recurrence relations: = + = + for n ≥ 1, = + = for n ≥ 2.Each of these relations can be proved by mathematical induction.From the second equation, we can deduce Goldbach's theorem (named after Christian Goldbach): no two Fermat numbers share a common integer factor greater than 1.

  4. Fermat's theorem on sums of two squares - Wikipedia

    en.wikipedia.org/wiki/Fermat's_theorem_on_sums_of...

    Fermat's theorem on sums of two squares is strongly related with the theory of Gaussian primes.. A Gaussian integer is a complex number + such that a and b are integers. The norm (+) = + of a Gaussian integer is an integer equal to the square of the absolute value of the Gaussian integer.

  5. Fermat's theorem - Wikipedia

    en.wikipedia.org/wiki/Fermat's_theorem

    The works of the 17th-century mathematician Pierre de Fermat engendered many theorems. Fermat's theorem may refer to one of the following theorems: Fermat's Last Theorem, about integer solutions to a n + b n = c n; Fermat's little theorem, a property of prime numbers; Fermat's theorem on sums of two squares, about primes expressible as a sum of ...

  6. Algebraic number theory - Wikipedia

    en.wikipedia.org/wiki/Algebraic_number_theory

    The formula, which Jacobi called a result "touching the utmost of human acumen", opened the way for similar results regarding more general number fields. [5] Based on his research of the structure of the unit group of quadratic fields , he proved the Dirichlet unit theorem , a fundamental result in algebraic number theory.

  7. Factorization - Wikipedia

    en.wikipedia.org/wiki/Factorization

    In this factorization, the rational number is called the content, and the primitive polynomial is the primitive part. The computation of this factorization may be done as follows: firstly, reduce all coefficients to a common denominator, for getting the quotient by an integer q of a polynomial with integer

  8. List of number theory topics - Wikipedia

    en.wikipedia.org/wiki/List_of_number_theory_topics

    Prime factor. Table of prime factors; Formula for primes; Factorization. ... Proofs of Fermat's little theorem; Fermat quotient; Euler's totient function. Noncototient;

  9. Fermat's Last Theorem - Wikipedia

    en.wikipedia.org/wiki/Fermat's_Last_Theorem

    Thus, to prove that Fermat's equation has no solutions for n > 2, it would suffice to prove that it has no solutions for at least one prime factor of every n. Each integer n > 2 is divisible by 4 or by an odd prime number (or both). Therefore, Fermat's Last Theorem could be proved for all n if it could be proved for n = 4 and for all odd primes p.