anonymous
  • anonymous
Find the smallest positive integer n such that every digit of 15n is 0 or 8.
Mathematics
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

dumbcow
  • dumbcow
well n must be even so that 15n ends in zero i found n=592 works, not sure how to prove it
anonymous
  • anonymous
I think i figured it out... not sure if this is the right proof though:
anonymous
  • anonymous
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)

Looking for something else?

Not the answer you are looking for? Search for more explanations.