Fraction

Number Theory Level pending

Denote \(\overline{Y,X} \) as a decimal number by placing \(Y\) and \(X\) as the fractional part and integer part of this decimal number, respectively. For example, if \(X = 301, Y = 622\), then \(\overline{Y,X} = 622.301\).

If \(x\) and \(y\) are coprime positive integers, find the maximum value of \(x+y\) such that \( \dfrac xy = \overline{y,x} \) is satisfied.

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