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Seventh Term Settlement (Posted on 2016-07-22) Difficulty: 3 of 5
Each of A(1), A(2),..., A(7) is a positive integer such that:

(i) A(6) = 144, and

(ii) A(n+3) = A(n+2)(A(n+1)+A(n)), for n = 1,2,3,4

Find A(7)

No Solution Yet Submitted by K Sengupta    
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no bad equations | Comment 6 of 10 |
Calling the first 3 terms x,y,z to minimize the use of parentheses and subscripts and building up the next terms I get A(6) = 144 = z^2 * (x+y)(x+y+1)(y+z), making z=12,6,4,3,2,1.

The first two values are too big, the next two don't give a result containing factors that are consecutive, and the last two give the previously cited answers:  (x,y,z) = (2,1,2) and (7,1,1).


  Posted by xdog on 2016-07-22 12:41:08
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