Coin problem

Common card · No. 285382

In mathematics, the coin problem (also referred to as the Frobenius coin problem or Frobenius problem, after the mathematician Ferdinand Frobenius) is a mathematical problem that asks for the largest monetary amount that cannot be obtained using only coins of specified denominations. For example, the largest amount that cannot be obtained using only coins of 3 and 5 units is 7 units. The solution to this problem for a given set of coin denominations is called the Frobenius number of the set. The Frobenius number exists as long as the set of coin denominations is setwise coprime. There is an explicit formula for the Frobenius number when there are only two different coin denominations, x {\displaystyle x} and y {\displaystyle y} , where the greatest common divisor of these two numbers is 1: x y − x − y {\displaystyle xy-x-y...

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