perplexus.info :: Sequences : Seventh Term Settlement

Seventh Term Settlement (Posted on 2016-07-22)

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)

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

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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