How Rademacher Derived His Formula for Partitioning Integers

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Can anyone sketch out how Rademacher wound up with his formula for the number of ways to partition an integer? Or at least explain why the number 24 shows up in it?

(In the graphic link below, the A coefficients are themselves defined as a certain rather complicated sum of exponentials to the base e.)
 

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Yes, Nate. In fact I grabbed the formula image file from that very page that you linked. I first came upon the formula in a layman's book on number theory by John Conway, but that book didn't offer a derivation if I recall.
 
Reminds of the solution to the third degree equation!
 
Bumping this up in case some of the newer members can provide some insight.
 
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This is the question, I understand the concept, in ##\mathbb{Z_n}## an element is a is a unit if and only if gcd( a,n) =1. My understanding of backwards substitution, ... i have using Euclidean algorithm, ##471 = 3⋅121 + 108## ##121 = 1⋅108 + 13## ##108 =8⋅13+4## ##13=3⋅4+1## ##4=4⋅1+0## using back-substitution, ##1=13-3⋅4## ##=(121-1⋅108)-3(108-8⋅13)## ... ##= 121-(471-3⋅121)-3⋅471+9⋅121+24⋅121-24(471-3⋅121## ##=121-471+3⋅121-3⋅471+9⋅121+24⋅121-24⋅471+72⋅121##...
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