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For the Frobenius Coin Problem, where $n = 3$

http://en.wikipedia.org/wiki/Coin_problem

Does anyone know a proof for Davidson's formula? The one that states that the lower bound for the Frobenius number is $$\sqrt{3 a_1 a_2 a_3}-a_1-a_2-a_3$$

Also, any links on proofs and duscussions on the other lower bound formulas like Selmer and Beyer's and Rodseth's?

Gerry Myerson
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andypls
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  • See http://math.stackexchange.com/questions/865024/something-related-to-frobenius-coin-problem-chicken-mcnugget-theorem/865267#865267 – deinst Feb 27 '15 at 14:34
  • Maybe you want to take a look at this: http://www.math.ethz.ch/~blatter/geomfrob.pdf – Christian Blatter Feb 27 '15 at 14:47
  • Quite confusing, is the lower bound really $$\sqrt{3a_1 a_2 a_3} - a_1 - a_2 - a_3 $$ or is it just $$\sqrt{3a_1 a_2 a_3}$$ as deinst's post states? – andypls Feb 28 '15 at 02:09
  • Have you tried following the links at the Wikipedia page? – Gerry Myerson Feb 28 '15 at 08:17
  • @GerryMyerson I checked out Davison's paper (at the Wiki links) and it says that the lower bound is just $$\sqrt{a_1 a_2 a_3}$$ I'll just test it out on small cases to make sure. (And if ever, edit the Wikipedia page) – andypls Feb 28 '15 at 12:29

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