\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2010a.00428}
\itemau{Holshouser, Arthur; Reiter, Harold}
\itemti{On a problem of Arthur Engel.}
\itemso{Math. Compet. 22, No. 1, 38-58 (2009).}
\itemab
From the introduction: Problem 21, page 10 of the book ``Problem Solving Strategies'' by Arthur Engel (Springer 1998; ME 1998a.00216) states: Three integers $a, b, c$ are written on a blackboard. Then one of the integers is erased and replaced by the sum of the other two diminished by 1. This operation is repeated many times with the final result 17, 1967, 1983. Could the initial numbers be (a) 2, 2, 2, (b) 3, 3, 3? This paper develops a mathematical context for a class of problems that includes this one and solves them.
\itemrv{~}
\itemcc{I30 F60 H60}
\itemut{integer triplets; Fibonacci set; divisibility; GCD; matrices; binary tree; proofs; matrix products; closed form; recursive number sequences}
\itemli{}
\end