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Floor function

Source: Indonesia Mathematics Olympiad 2005 Day 2 Problem 5

June 2, 2008
functionfloor functionnumber theory proposednumber theory

Problem Statement

For an arbitrary real number x x, ⌊x⌋ \lfloor x\rfloor denotes the greatest integer not exceeding x x. Prove that there is exactly one integer m m which satisfy \displaystyle m\minus{}\left\lfloor \frac{m}{2005}\right\rfloor\equal{}2005.
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