AMC 10 Step by Step
2013 AMC 10AProblem 19P16-20~4 minPrint

In base 1010 , the number 20132013 ends in the digit 33 . In base 99 , on the other hand, the same number is written as (2676)9(2676)_{9} and ends in the digit 66 . For how many positive integers bb does the base- bb -representation of 20132013 end in the digit 33 ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.