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Integers only (Posted on 2014-03-31) Difficulty: 3 of 5
What is the smallest pair (a1,a2) of integers (a1, less than a2) to provide a list of 24 integers using
a recurrent function a(n)=(a(n-1)+a(n-2))/2?

See The Solution Submitted by Ady TZIDON    
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Some Thoughts re: Generalised approach Comment 7 of 7 |
(In reply to Generalised approach by Harry)

Excellent finding, Harry!


I thought that your main points got buried, so I am reposting them.   (No original work on my part was done)

You astutely wrote:

So for a24 to be an integer, (a2  a1) must be divisible by 222

If only positive integers are allowed for (a1, a2) then choose (1, 222 + 1).

If zero is allowed then (0, 222) is best, as Jer recommended.

If all integers are allowed then (-221, 221) have the smallest abs. values

  Posted by Steve Herman on 2014-04-01 08:53:55
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