Find the greatest integer such that and the last three digits of (ones, tens, and hundreds) are the same as integer itself.

Source: mathcontest.olemiss.edu 4/29/2013

**SOLUTION**

Let be the three digits of where is the hundreds digit, the tens digit, and the ones digit.

We want to end in 1 so that .

The ones digit is either or .

ending in is a necessary condition*. *For example,

Multiply

is the largest integer such that and the last three digits of match the digits of

**Answer**:

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