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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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Some Thoughts Is an algebraic solution likely | Comment 5 of 10 |
I arrived at the same solutions as Charlie with a program.  It's pretty simple so show that if any of the first 3 terms are too large then A(6) will exceed 144.

An attempt at solving this analytically with algebra leads quickly to a brick wall of a formula: a 5th degree polynomial Diophantine equation in three variables with 10 terms.  I won't even type it out.

It is quadratic in A(1) but cubic in A(2) and quartic in A(3).

Yuck.


  Posted by Jer on 2016-07-22 11:16:48
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