Determine the minimum value of a positive integer N such that:
o N has the form: 97.......97, and:
o N is divisible by 99
(In reply to
re(2): solution by Charlie)
Am I missing something here? If we assume the ... can by a string of any length, I find the minimum solution to be 970497. Using the same methodology from your first comment, a number is divisible by 99 if it is divisible by both 9 and 11. Given that it starts and ends with 97, it must have at least 5 digits, since the digital sum of 9797 is not divisible by 9.
For a 5 digit number 97x97 to be divisible by 9, x must equal 4. But then (9 + 4 + 7) - (7 + 9) = 4, so 97497 is not divisible by 11. So the smallest such integer must have at least 6 digits.
The smallest possible 6 digit integer would then by of the form 970x97. As before, x must equal 4 to ensure divisibility by 9, and in this case (9 + 0 + 9) - (7 + 4 + 7) = 0, so 970497 is divisible by 11 (and thus 99). Indeed, 99 × 9703 = 970497.
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Posted by H M
on 2021-12-12 16:49:56 |
re(3): solution
