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All the nines (Posted on 2022-04-07) Difficulty: 3 of 5

Let a be a prime of the form (2n+1), and let b be a prime of the form (2a+1), such that 1/b has an even period of length 2a, i.e. 0 followed by 2a decimal digits.

The 'splitadd' function splits these 2a digits into equal halves and adds them.

To give an (imaginary) example, say 1/b was 0.0123456789, then 'splitadd' would produce 01234+56789, and add these for a value of 58023.

Show that the result of the 'splitadd' function is always (10^a-1), or find a counterexample.

No Solution Yet Submitted by broll    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(3): possible computer solution(s) | Comment 5 of 9 |
(In reply to re(2): possible computer solution(s) by broll)

Indeed you are correct. The program was running with digits set to too small a number to represent the numbers accurately. 431 863 should have been noted "verified" as indeed the splitting of this actual period and summing results in 10^a-1.
  Posted by Charlie on 2022-04-09 12:05:36

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