My lucky number

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I don't know should I ask in Puzzling or not. Sorry for that if I'm wrong! And my question is, I have a lucky number that has four digits which the first three numbers and the last three numbers are perfect square and my lucky number's digits are different. I found the number but I couldn't figure out a mathematical way to solve. Appreciate your help!

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A possible solution is the number $7841$ since : $784=28^2$ and $841=29^2$.

An inspection to a table of squares shows that this is the only possible solution.