Michael's number

Algebra Level 3

For a positive four-digit integer n,n, let T(n)T(n) be the number created by swapping the hundreds and thousands digits of nn and swapping the tens and units digits of n.n. There is a unique integer MM such that T(M)=4M.T(M)= 4M. What are the last three digits of MM?

This problem is posed by Michael T.

Details and assumptions

For example, T(1234)=2143T(1234)=2143 and T(1508)=5180.T(1508) = 5180.

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