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OMK 2010

Source: Malaysia National Olympiad 2010 Muda Category Problem 8

June 4, 2011
floor functionnumber theory unsolvednumber theory

Problem Statement

For any number xx, let ⌊x⌋\lfloor x\rfloor denotes the greatest integer less than or equal to xx. A sequence a1,a2,⋯a_1,a_2,\cdots is given, where an=⌊2n+12⌋.a_n=\left\lfloor{\sqrt{2n}+\dfrac{1}{2}}\right\rfloor. How many values of kk are there such that ak=2010a_k=2010?
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