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  2. Quadratic reciprocity - Wikipedia

    en.wikipedia.org/wiki/Quadratic_reciprocity

    Gauss published the first and second proofs of the law of quadratic reciprocity on arts 125–146 and 262 of Disquisitiones Arithmeticae in 1801.. In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers.

  3. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    Terms with infinitely many sine factors would necessarily be equal to zero. When only finitely many of the angles are nonzero then only finitely many of the terms on the right side are nonzero because all but finitely many sine factors vanish. Furthermore, in each term all but finitely many of the cosine factors are unity.

  4. Modulo (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Modulo_(mathematics)

    Modulo is a mathematical jargon that was introduced into mathematics in the book Disquisitiones Arithmeticae by Carl Friedrich Gauss in 1801. [3] Given the integers a, b and n, the expression "a ≡ b (mod n)", pronounced "a is congruent to b modulo n", means that a − b is an integer multiple of n, or equivalently, a and b both share the same remainder when divided by n.

  5. Factorization - Wikipedia

    en.wikipedia.org/wiki/Factorization

    In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is an integer factorization of 15, and (x – 2)(x + 2) is a polynomial ...

  6. Geometric series - Wikipedia

    en.wikipedia.org/wiki/Geometric_series

    For example, the series + + + is a geometric series with common ratio ⁠ ⁠, which converges to the sum of ⁠ ⁠. Each term in a geometric series is the geometric mean of the term before it and the term after it, in the same way that each term of an arithmetic series is the arithmetic mean of its neighbors.

  7. Alabama's College Football Playoff ranking illustrates ...

    www.aol.com/alabamas-college-football-playoff...

    Alabama looks in line for a College Football Playoff berth and that's a nod to the power of the SEC and Big Ten compared to other conferences.

  8. January-March Temperature Forecast Features Milder South And ...

    www.aol.com/january-march-temperature-forecast...

    Here's how the temperature outlook is shaping up across the U.S. for the first three months of 2025.

  9. Quadratic sieve - Wikipedia

    en.wikipedia.org/wiki/Quadratic_sieve

    The quadratic sieve attempts to find pairs of integers x and y(x) (where y(x) is a function of x) satisfying a much weaker condition than x 2 ≡ y 2 (mod n). It selects a set of primes called the factor base , and attempts to find x such that the least absolute remainder of y ( x ) = x 2 mod n factorizes completely over the factor base.