How is Frobenius number calculated?

Since we previously saw that n is representable whenever n>ab−a−b n > a b − a − b , we have found the Frobenius number. If a and b are relatively prime, then the Frobenius number g(a,b)=ab−a−b.

What is the largest number of McNuggets that Cannot be ordered?

43
What is the largest number for which it is impossible to purchase exactly that number of McNuggets? The answer is 43. Solution For any desired number if it is divisible by 3 it can easily be made with 6 and 9 packs, except if the number is 3 itself.

How do you prove chicken McNugget Theorem?

Proof of the Chicken McNugget Theorem

Chicken McNugget Theorem: For relatively prime positive integers a and b, the number M=ab-a-b cannot be expressed as ax+by for any nonnegative integers x and y.
Bézout’s Identity: If a and b are integers, then there exist integers x,y such that ax+by=gcd(a,b).

What is the Frobenius method?

. In mathematics, the method of Frobenius, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a second-order ordinary differential equation of the form . . which will not be solvable with regular power series methods if either p(z)/z or q(z)/z2 are not analytic at z = 0.

How do you find the Frobenius series?

We seek a Frobenius-type solution of the form y = ∞ ∑ k = 0akxk + r. We plug this y into equation (7.3.26). We collect terms and write everything as a single series. The obtained series must be zero.

How many Frobenius-type solutions do you need to solve a problem?

The main idea is to find at least one Frobenius-type solution. If we are lucky and find two, we are done. If we only get one, we either use the ideas above or even a different method such as reduction of order (Exercise 2.1.8) to obtain a second solution.

What is the Frobenius-type solution of Y = XR ∞ ∑ K?

y = xr ∞ ∑ k = 0akxk. A solution of this form is called a Frobenius-type solution. The method usually breaks down like this. We seek a Frobenius-type solution of the form y = ∞ ∑ k = 0akxk + r. We plug this y into equation (7.3.26).