On the problem

Author:
R. E. Crandall

Journal:
Math. Comp. **32** (1978), 1281-1292

MSC:
Primary 10A99

MathSciNet review:
0480321

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Abstract: It is an open conjecture that for any positive odd integer *m* the function

*h*. Here we show that the number of which satisfy the conjecture is at least for a positive constant

*c*. A connection between the validity of the conjecture and the diophantine equation is established. It is shown that if the conjecture fails due to an occurrence , then

*k*is greater than 17985. Finally, an analogous "" problem is settled for certain pairs .

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1978-0480321-3

Keywords:
Algorithm,
diophantine equation

Article copyright:
© Copyright 1978
American Mathematical Society