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The Frobenius number exists as long as the set of coin denominations is setwise coprime. There is an explicit formula for the Frobenius number when there are only two different coin denominations, and , where the greatest common divisor of these two numbers is 1: . If the number of coin denominations is three or more, no explicit formula is known.
The following algorithm, known as Rödseth's algorithm, [10] [11] can be used to compute the Frobenius number of a numerical semigroup S generated by {a 1, a 2, a 3} where a 1 < a 2 < a 3 and gcd ( a 1, a 2, a 3) = 1.
In mathematics, specifically in representation theory, the Frobenius formula, introduced by G. Frobenius, computes the characters of irreducible representations of the symmetric group S n. Among the other applications, the formula can be used to derive the hook length formula .
The postage stamp problem (also called the Frobenius Coin Problem and the Chicken McNugget Theorem [1]) is a mathematical riddle that asks what is the smallest postage value which cannot be placed on an envelope, if the latter can hold only a limited number of stamps, and these may only have certain specified face values.
A Markov number or Markoff number is a positive integer x, ... one may permute the 3 numbers x,y,z, ... as remarked by Frobenius in 1913, [4] ...
3.3 Frobenius primality test. 3.4 ... A rather simple optimization is to test divisibility by 2 and by just the odd numbers between 3 ... for every composite number n ...
In number theory, a Frobenius pseudoprime is a pseudoprime, whose definition was inspired by the quadratic Frobenius test described by Jon Grantham in a 1998 preprint and published in 2000. [ 1 ] [ 2 ] Frobenius pseudoprimes can be defined with respect to polynomials of degree at least 2, but they have been most extensively studied in the case ...
The Fano plane. The smallest example is the symmetric group on 3 points, with 6 elements. The Frobenius kernel K has order 3, and the complement H has order 2.; For every finite field F q with q (> 2) elements, the group of invertible affine transformations +, acting naturally on F q is a Frobenius group.