English Dictionary

Frobenius number

名詞

For a given set of coprime positive integers, the greatest integer that cannot be expressed as a linear combination (with nonnegative integer coefficients) of its elements.

日本語の意味

与えられた互いに素な正整数からなる集合に対して、その集合の要素を非負の整数の係数で線形結合して表現できない最大の整数

When given the coin denominations 4 and 7, the Frobenius number is 17, meaning it is the largest amount that cannot be formed by nonnegative integer combinations of those coins.

硬貨の額面が4と7のとき、フロベニウス数は17であり、これはそれらの数の非負整数係数による線形結合として表せない最大の整数、すなわちそれらの硬貨で作れない最大の金額を意味する。

意味（1）

For a given set of coprime positive integers, the greatest integer that cannot be expressed as a linear combination (with nonnegative integer coefficients) of its elements.

The Frobenius number of 2 and 5 is 3, since 3 cannot be formed as a sum of twos and fives while every larger integer can.

Frobenius numbers （ plural ）