id: 05667641
dt: j
an: 2010a.00428
au: Holshouser, Arthur; Reiter, Harold
ti: On a problem of Arthur Engel.
so: Math. Compet. 22, No. 1, 38-58 (2009).
py: 2009
pu: AMT Publishing, Australian Mathematics Trust, University of Canberra,
Canberra
la: EN
cc: I30 F60 H60
ut: integer triplets; Fibonacci set; divisibility; GCD; matrices; binary tree;
proofs; matrix products; closed form; recursive number sequences
ci: ME 1998a.00216
li:
ab: 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.
rv: