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Positive Frobenius Numbers of Three Arguments

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December 30, 2016
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Let ... , ... , ... be three positive integers with ... . It is well-known that all sufficiently large integers are representable as positive linear combinations of ... , ... , ... . Consider ... , the positive Frobenius number of ... , ... , ... , defined to be the largest integer not representable as a positive linear combination of ... , ... , ... . Then ... is the usual Frobenius number, that is, the largest integer not representable as a non-negative linear combination ... , ... , ... . ( ... differs from the positive Frobenius number ... in that multipliers for linear combinations of larger integers are allowed to be zero.) The function ... corresponds to the Mathematica built-in function ... . We assume that ... , ... , ... are pairwise prime. This Demonstration computes and represents ... in three ways as positive linear combinations of (1) ... , ... , (2) ... , ... , and (3) ... , ... .

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      Let ... , ... , ... be three positive integers with ... . It is well-known that all sufficiently large integers are representable as positive linear combinations of ... , ... , ... . Consider ... , the positive Frobenius number of ... , ... , ... , defined to be the largest integer not representable as a positive linear combination of ... , ... , ... . Then ... is the usual Frobenius number, that is, the largest integer not representable as a non-negative linear combination ... , ... , ... . ( ... differs from the positive Frobenius number ... in that multipliers for linear combinations of larger integers are allowed to be zero.) The function ... corresponds to the Mathematica built-in function ... . We assume that ... , ... , ... are pairwise prime. This Demonstration computes and represents ... in three ways as positive linear combinations of (1) ... , ... , (2) ... , ... , and (3) ... , ... .
      ↓http://demonstrations.wolfram.com/PositiveFrobeniusNumbersOfThreeArguments/

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