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

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dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1well n must be even so that 15n ends in zero i found n=592 works, not sure how to prove it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I think i figured it out... not sure if this is the right proof though:

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Let 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)
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