A number theory problem by Budi Utomo

Number Theory Level 3

\[\dfrac{21197}{2097} = a + \dfrac1{b + \dfrac2{c + \dfrac3{d + \dfrac4{e+5}}}} \]

Given that \(a,b,c,d\) and \(e\) are positive integers satisfying the equation above, and if the value of the fraction below

\[ 1 + \dfrac a{2 + \dfrac b{3 + \dfrac c{4 + \dfrac d{5+e}}}} \]

is equal to \( \dfrac xy\), where \(x\) and \(y\) are coprime positive integers, find \(x+y\).


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