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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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Some Thoughts Not sure | Comment 1 of 9

16777181 is a number under 30 million but there seem to be one too many repeats of the process.

2097117 seems to comply with the requirements of the problem, but is not a unique solution below 30 million.

  Posted by broll on 2016-04-06 09:37:19
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