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Next year vs the current year (Posted on 2015-02-25) Difficulty: 2 of 5
2016k divides 2016!2016.

For how many positive values of the integer k is the above true?

What would be your answer if the number 2016 was replaced by 2015 in all 2016's appearances?

No Solution Yet Submitted by Ady TZIDON    
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re: Paper and Pencil solution, part (a) / part (b) | Comment 3 of 5 |
(In reply to Paper and Pencil solution, part (a) by Steve Herman)

My solution method is essentially the same, so I'll just share the result to using 2015:


2015 = 5*13*31

So 31 will definitely be the limiting factor.  
2015!^2015 is divisible by 31^(67*2015) = 31^135005.

The final answer to the question is 135005/1 =135005

Edited on February 25, 2015, 11:40 am
  Posted by Jer on 2015-02-25 11:04:56

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