Optimal Bounds for the Length of Rational Collatz Cycles
نویسنده
چکیده
We consider the arithmetics of Collatz cycles in Q(2)]. In particular , we prove optimal estimates for the length of a cycle in terms of its minimum. As an application, we derive an improved version of Eliahou's criterion , and we show that the length of (integer) Collatz cycles which do not contain 1, is at least 102 225 496 provided the Collatz conjecture is veriied for all initial values x 0 212 366 032 807 211.
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تاریخ انتشار 1997