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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