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  2. Modulo - Wikipedia

    en.wikipedia.org/wiki/Modulo

    For example, the expression "5 mod 2" evaluates to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0, because 9 divided by 3 has a quotient of 3 and a remainder of 0. Although typically performed with a and n both being integers, many computing systems now allow other types of numeric operands.

  3. Modular arithmetic - Wikipedia

    en.wikipedia.org/wiki/Modular_arithmetic

    Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...

  4. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    For any integer n, n ≡ 1 (mod 2) if and only if ⁠ 3n + 1 / 2 ⁠ ≡ 2 (mod 3). Equivalently, ⁠ 2 n − 1 / 3 ⁠ ≡ 1 (mod 2) if and only if n ≡ 2 (mod 3) . Conjecturally, this inverse relation forms a tree except for a 1–2 loop (the inverse of the 1–2 loop of the function f(n) revised as indicated above).

  5. Fermat number - Wikipedia

    en.wikipedia.org/wiki/Fermat_number

    That 641 is a factor of F 5 can be deduced from the equalities 641 = 2 7 × 5 + 1 and 641 = 2 4 + 5 4. It follows from the first equality that 2 7 × 5 ≡ −1 (mod 641) and therefore (raising to the fourth power) that 2 28 × 5 4 ≡ 1 (mod 641). On the other hand, the second equality implies that 5 4 ≡ −2 4 (mod 641

  6. Multiplicative order - Wikipedia

    en.wikipedia.org/wiki/Multiplicative_order

    The multiplicative order of a number a modulo n is the order of a in the multiplicative group whose elements are the residues modulo n of the numbers coprime to n, and whose group operation is multiplication modulo n. This is the group of units of the ring Zn; it has φ (n) elements, φ being Euler's totient function, and is denoted as U (n) or ...

  7. When is the NFL trade deadline? Date, time for 2024 cutoff - AOL

    www.aol.com/nfl-trade-deadline-date-time...

    This year's NFL trade deadline is set for Tuesday, Nov. 5 – Election Day – at 4 p.m. ET. After that time, the 32 NFL teams will not be allowed to complete any more trades until the official ...

  8. Multiplicative group of integers modulo n - Wikipedia

    en.wikipedia.org/wiki/Multiplicative_group_of...

    n. In modular arithmetic, the integers coprime (relatively prime) to n from the set of n non-negative integers form a group under multiplication modulo n, called the multiplicative group of integers modulo n. Equivalently, the elements of this group can be thought of as the congruence classes, also known as residues modulo n, that are coprime to n.

  9. Montgomery modular multiplication - Wikipedia

    en.wikipedia.org/wiki/Montgomery_modular...

    The Montgomery forms of 7 and 15 are 70 mod 17 = 2 and 150 mod 17 = 14, respectively. Their product 28 is the input T to REDC, and since 28 < RN = 170, the assumptions of REDC are satisfied. To run REDC, set m to (28 mod 10) ⋅ 7 mod 10 = 196 mod 10 = 6. Then 28 + 6 ⋅ 17 = 130, so t = 13.

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