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.
(In reply to Help from a negative (solution)
by Brian Smith)
....To get the positive integer solution sought add 8^8 to x_0.
Then x_0 = 8^8-35 = 16777181 and by repeated iteration x_8 = 7^8-35 = 5764766.
no, you don't see my numbers