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  2. Remainder - Wikipedia

    en.wikipedia.org/wiki/Remainder

    In this case, s is called the least absolute remainder. [3] As with the quotient and remainder, k and s are uniquely determined, except in the case where d = 2n and s = ± n. For this exception, we have: a = k⋅d + n = (k + 1)d − n. A unique remainder can be obtained in this case by some convention—such as always taking the positive value ...

  3. Modulo - Wikipedia

    en.wikipedia.org/wiki/Modulo

    In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.

  4. Euclidean division - Wikipedia

    en.wikipedia.org/wiki/Euclidean_division

    In the above theorem, each of the four integers has a name of its own: a is called the dividend, b is called the divisor, q is called the quotient and r is called the remainder. The computation of the quotient and the remainder from the dividend and the divisor is called division, or in case of ambiguity, Euclidean division.

  5. Modular arithmetic - Wikipedia

    en.wikipedia.org/wiki/Modular_arithmetic

    In fact, x ≡ b m n −1 m + a n m −1 n (mod mn) where m n −1 is the inverse of m modulo n and n m −1 is the inverse of n modulo m. Lagrange's theorem: If p is prime and f (x) = a 0 x d + ... + a d is a polynomial with integer coefficients such that p is not a divisor of a 0, then the congruence f (x) ≡ 0 (mod p) has at most d non ...

  6. 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.

  7. Chinese remainder theorem - Wikipedia

    en.wikipedia.org/wiki/Chinese_remainder_theorem

    Suppose that x and y are both solutions to all the congruences. As x and y give the same remainder, when divided by n i, their difference xy is a multiple of each n i. As the n i are pairwise coprime, their product N also divides xy, and thus x and y are congruent modulo N.

  8. Why is X still called Twitter? - AOL

    www.aol.com/why-t-stop-calling-twitter-210004909...

    The X rebrand may have a harder journey, Withey said, due to it being an unusual case of a high equity brand — one that was a cultural force for well over a decade — being renamed overnight.

  9. Polynomial long division - Wikipedia

    en.wikipedia.org/wiki/Polynomial_long_division

    x 2 has been divided leaving no remainder, and can therefore be marked as used. The result x is then multiplied by the second term in the divisor −3 = −3x. Determine the partial remainder by subtracting 0x − (−3x) = 3x. Mark 0x as used and place the new remainder 3x above it.