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  2. Verhoeff algorithm - Wikipedia

    en.wikipedia.org/wiki/Verhoeff_algorithm

    This is actually a single permutation (1 5 8 9 4 2 7 0)(3 6) applied iteratively; i.e. p(i+j,n) = p(i, p(j,n)). The Verhoeff checksum calculation is performed as follows: Create an array n out of the individual digits of the number, taken from right to left (rightmost digit is n 0, etc.). Initialize the checksum c to zero.

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  4. Modular multiplicative inverse - Wikipedia

    en.wikipedia.org/wiki/Modular_multiplicative_inverse

    X ≡ 6 (mod 11) has common solutions since 5,7 and 11 are pairwise coprime. A solution is given by X = t 1 (7 × 11) × 4 + t 2 (5 × 11) × 4 + t 3 (5 × 7) × 6. where t 1 = 3 is the modular multiplicative inverse of 7 × 11 (mod 5), t 2 = 6 is the modular multiplicative inverse of 5 × 11 (mod 7) and t 3 = 6 is the modular multiplicative ...

  5. Branch and cut - Wikipedia

    en.wikipedia.org/wiki/Branch_and_cut

    This description assumes the ILP is a maximization problem.. The method solves the linear program without the integer constraint using the regular simplex algorithm.When an optimal solution is obtained, and this solution has a non-integer value for a variable that is supposed to be integer, a cutting plane algorithm may be used to find further linear constraints which are satisfied by all ...

  6. Modulo - Wikipedia

    en.wikipedia.org/wiki/Modulo

    If p is a prime number which is not a divisor of b, then ab p−1 mod p = a mod p, due to Fermat's little theorem. Inverse: [(−a mod n) + (a mod n)] mod n = 0. b −1 mod n denotes the modular multiplicative inverse, which is defined if and only if b and n are relatively prime, which is the case when the left hand side is defined: [(b −1 ...

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  8. US announces $5.9 billion in military and budget aid to Ukraine

    www.aol.com/news/biden-announces-2-5-billion...

    A U.S. official said the $3.4 billion in budget funding brings the total in U.S. budget aid to Ukraine to just over $30 billion since Russia's invasion in February 2022.

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