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.
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