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Tenacious Divisibility Treat (Posted on 2016-04-06) Difficulty: 2 of 5
A positive integer less than 30 million is such that if we subtract 5 from it – the resulting number is divisible by 8.

At the first step, from the number (considered originally) diminished by 5 - we subtract the eighth part. We then obtain a number that also becomes divisible by 8 after 5 is subtracted from it.

At the second step, we derive another in the same way, namely by subtracting a eighth part from the number at the end of the first step diminished by 5. The resulting number is also divisible by 8 after subtracting 5.

The operation concludes at 8th step given that at the end of 7th step we get a number that is divisible by 8 after after subtracting 5.

Determine the positive integer initially before the first step.

*** The resulting number at the end of 8th step is NOT necessarily divisible by 8 after subtracting 5.

No Solution Yet Submitted by K Sengupta    
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Hints/Tips re: Help from a negative (solution) | Comment 5 of 9 |
(In reply to Help from a negative (solution) by Brian Smith)

....To get the positive integer solution sought add 8^8 to x_0.  

bad  idea

  Then x_0 = 8^8-35 = 16777181 and by repeated iteration x_8 = 7^8-35 = 5764766. 

 no,  you don't     see my numbers

  Posted by Ady TZIDON on 2016-04-06 12:54:42
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