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On a conjecture of Crandall concerning the $qx+1$ problem

Authors: Zachary Franco and Carl Pomerance
Journal: Math. Comp. 64 (1995), 1333-1336
MSC: Primary 11B83; Secondary 11B05
MathSciNet review: 1297468
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Abstract: R. E. Crandall has conjectured that for any odd integer $q > 3$, there is a positive integer m whose orbit in the "$qx + 1$ problem" does not contain 1. We show that this is true for almost all odd numbers q, in the sense of asymptotic density.

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Keywords: <IMG WIDTH="62" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img2.gif" ALT="$3x + 1$"> problem, <IMG WIDTH="61" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$qx + 1$"> problem, Wieferich prime
Article copyright: © Copyright 1995 American Mathematical Society