für 44.10€ kaufen ··· 9783845405131 ··· 10361132218 ··· Given integer-valued relatively prime `coins` a1 a2 ::: ak, the Frobenius number is the largest integer n such that the linear diophantine equation a1m1 + a2m2 + ::: + akmk = n has no solution in non-negative integers m1 m2 ::: mk. We denote by g(a1 ::: ak) the largest integer value not attainable by this coin system. That is to say that any integer x greater than the Frobenius number g(a1 ::: ak) has a representation x = a1x1 + a2x2 + ::: + akxk by a1 a2 ::: ak for some non-negative integers x1 x2 ::: xk. We say x is representable by a1 a2 ::: ak. While it is obvious that there are representable positive integers and non-representable positive integers, must there be a largest non-representable integer Maybe there are indefinitely large non-representable integers for a1 a2 ::: ak with gcd (a1 a2 ::: ak) = 1. This notion of whether or not the Frobenius number is well-defined will be the first bit of mathematics we look at in this paper. Proposition 1.1. The Frobenius number g(a1 ::: ak) is well-defined. Proof. Given a1 a2 ::: ak with gcd (a1 a2 ::: ak) = 1, the extended Euclidean algorithm gives that there exist m1 m2 ::: mk 2 Z such that... Hersteller: LAP Lambert Academic Publishing Marke: LAP Lambert Academic Publishing EAN: 9783845405131 Kat: Hardcover/Naturwissenschaften, Medizin, Informatik, Technik/Mathematik Lieferzeit: Sofort lieferbar Versandkosten: Ab 20¤ Versandkostenfrei in Deutschland Icon: https://www.inforius-bilder.de/bild/?I=Dc4Y2swSLCXzVkuZHBj0z%2FxIqBhIKGXhGHFNOxKHeJQ%3D Bild:
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