problemdescriptionthefrobeniusproblemisanoldprobleminmathematics，namedafterthegermanmathematiciankdxf (18491917 )。
Let a1，a2，…，an be integers larger than 1，withgreatestcommondivisor(gcd )1. thenitisknownthattherearefinitelymanyintegegegersterstelymantetegatetegrstttttttion thatcannotbeexpressedasalinearcombinationw1a1w2a 2…wnanusingintegercoefficientswi0.thelargestofsuchnonegativegersis of a1、a2、…、an(Denotedbyf(a1、a2、…、an ) ).so:f ) a1、a2、…、、、、和an ) isthelargestnonnegativeintegerthatcannotbeexpressedasanonnegativeintegerlinearcombinationofa 1、a2、…、an。
forn=2thereisasimpleformulaforf (a1，a2 ).However，forn3 itismuchmorecomplicated.forn=3onlyforsomespecialchoicesoialchoicesore