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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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On the $β€œ3x+1”$ problem
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by R. E. Crandall PDF
Math. Comp. 32 (1978), 1281-1292 Request permission


It is an open conjecture that for any positive odd integer m the function \[ C(m) = (3m + 1)/{2^{e(m)}},\] where $e(m)$ is chosen so that $C(m)$ is again an odd integer, satisfies ${C^h}(m) = 1$ for some h. Here we show that the number of $m \leqslant x$ which satisfy the conjecture is at least ${x^c}$ for a positive constant c. A connection between the validity of the conjecture and the diophantine equation ${2^x} - {3^y} = p$ is established. It is shown that if the conjecture fails due to an occurrence $m = {C^k}(m)$, then k is greater than 17985. Finally, an analogous "$qx + r$" problem is settled for certain pairs $(q,r) \ne (3,1)$.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Math. Comp. 32 (1978), 1281-1292
  • MSC: Primary 10A99
  • DOI:
  • MathSciNet review: 0480321