# 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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