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2^89 and 2^98 (Posted on 2024-01-09) Difficulty: 3 of 5
Find the smallest 89-digit integer which is a multiple of 289, and the smallest 98-digit integer which is a multiple of 298, both consisting solely of the digits 8 and 9.

  Submitted by K Sengupta    
Rating: 4.5000 (2 votes)
Solution: (Hide)
Part One: 89 digits
The answer is:
99999989998899889889988898999988888898989889899889988989999888898888999898998898989989888
Which when divided by 2^89 by a full precision calculator, yields:
161558697231614555082401092391961704994738678758575489807199124

Part Two: 98 digits.
The answer is:
99998898899999989998899889889988898999988888898989889899889988989999888898888999898998898989989888
Which when divided by 2^98 by a full precision calculator, yields:
315540887629433735182388126426444767830548314571752815633922913670677
By the way, the decimal answer to part two is simply: 999988988 concatenated with the answer for part one.

For an explanation, refer to the solution submitted by Larry in this location.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: Computer solutionAdy TZIDON2024-01-11 18:28:54
SolutionComputer solutionLarry2024-01-09 13:08:29
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