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:

 3 (100000+x)=10 x+1  7x=299999  x=42857



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