Question

Find the smallest positive integer n such that every digit of 15n is 0 or 8.

Answer 1

well n must be even so that 15n ends in zero

i found n=592 works, not sure how to prove it

Answer 2

I think i figured it out... not sure if this is the right proof though:

Answer 3

Let N=15n. Since the number N is divisible by 3 and 5, the sum of the digits must be divisible by 3, and the last digit must be zero or 5. if N consists only of digits 0 and 8, it follows that the last digit must be zero and the number of digits 8 contained in N must be a multiple of 3. Therefore the smallest number with these properties is N=8880, so n=N/15=592 is the smallest positive integer such that every digit of 15n is 8 or 0. (I THINK)