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Yearly Division (Posted on 2015-07-22) Difficulty: 3 of 5
Find the smallest number that, when divided successively by 15, 151, 1515 and 15151, leaves the remainders 1, 15, 151, and 1515 respectively.

No Solution Yet Submitted by K Sengupta    
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Solution solution Comment 1 of 1
The first number when that leaves 1 after division by 15 is 16.

Adding 15 until a number leaving 15 after division by 151, brings up 166.

15 and 151 are relatively prime, so we need to increase by 15*151 enought times to get a number with remainder 151 after division by 1515, and it's 4696.

The LCM of 15, 151 and 1515 is just 151*1515.  Adding as many of these to get a remainder of 1515 after division by 15151 brings us to the answer: 71150611. The mechanics done by:

   10   N=16
   20   while N @ 151<>15:N=N+15:wend
   30   print N
   40   Incr=15*151
   50   while N @ 1515<>151
   60     N=N+Incr
   70   wend
   80   print N
  140   Incr=151*1515
  150   while N @ 15151<>1515
  160     N=N+Incr
  170   wend
  180   print N



  Posted by Charlie on 2015-07-22 13:39:52
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