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On the same floor (Posted on 2016-11-22) Difficulty: 3 of 5
How many solutions (m,n positive integers only) are there for
floor(m/6)=floor(n/13) ?

List them.

No Solution Yet Submitted by Ady TZIDON    
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Solution Solutions per Integer | Comment 4 of 13 |
For any integer x, the equation floor(m/6)=x has 6 integer solutions 6x+k where k=0 to 5.  Similarly floor(n/13)=x has 13 integer solutions 13x+j where j=0 to 12.

Then the compound equation floor(m/6)=floor(n/13)=x has 6*13 = 78 solutions for every integer x.

  Posted by Brian Smith on 2016-11-22 13:37:25
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