Two identical five-digits

We have two identical five-digit numbers, but we don't know which ones. When we write one before the first and after the second one we get two six-digit numbers, one of which is three times the other. What are the numbers?

Correct result:

x =  42857

Solution:

$$\begin{gathered} 3\cdot (100000+x)=10\cdot x+1 \\ 7x=299999 \\ x=42857 \end{gathered}$$

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