<span style="font-family:Verdana;">The unsolved number theory problem known as the 3</span><i><i><span style="font-family:Verdana;">x</span></i><span st...<span style="font-family:Verdana;">The unsolved number theory problem known as the 3</span><i><i><span style="font-family:Verdana;">x</span></i><span style="font-family:Verdana;"></span></i><span style="font-family:Verdana;"> + 1 problem involves sequences of positive integers generated more or less at random that seem to always converge to 1. Here the connection between the first integer (</span><i><i><span style="font-family:Verdana;">n</span></i><span style="font-family:Verdana;"></span></i><span style="font-family:Verdana;">) and the last (</span><i><i><span style="font-family:Verdana;">m</span></i><span style="font-family:Verdana;"></span></i><span style="font-family:Verdana;">) of a 3</span><i><i><span style="font-family:Verdana;">x</span></i><span style="font-family:Verdana;"></span></i><span style="font-family:Verdana;"> + 1 sequence is analyzed by means of characteristic zero-one strings. This method is used to achieve some progress on the 3</span><i><i><span style="font-family:Verdana;">x</span></i><span style="font-family:Verdana;"></span></i><span style="font-family:Verdana;"> + 1 problem. In particular, the</span> long<span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;">standing conjecture that nontrivial cycles do not exist is virtually proved using probability theory.</span></span>展开更多
The author makes the claim to have a solution for the famous 3x + 1 problem. The key to its solution is a special proof that the term (3 + ε)<sup>r</sup> is a non-integer, as well as the use of properties...The author makes the claim to have a solution for the famous 3x + 1 problem. The key to its solution is a special proof that the term (3 + ε)<sup>r</sup> is a non-integer, as well as the use of properties of extremal points of a Collatz sequence.展开更多
文摘<span style="font-family:Verdana;">The unsolved number theory problem known as the 3</span><i><i><span style="font-family:Verdana;">x</span></i><span style="font-family:Verdana;"></span></i><span style="font-family:Verdana;"> + 1 problem involves sequences of positive integers generated more or less at random that seem to always converge to 1. Here the connection between the first integer (</span><i><i><span style="font-family:Verdana;">n</span></i><span style="font-family:Verdana;"></span></i><span style="font-family:Verdana;">) and the last (</span><i><i><span style="font-family:Verdana;">m</span></i><span style="font-family:Verdana;"></span></i><span style="font-family:Verdana;">) of a 3</span><i><i><span style="font-family:Verdana;">x</span></i><span style="font-family:Verdana;"></span></i><span style="font-family:Verdana;"> + 1 sequence is analyzed by means of characteristic zero-one strings. This method is used to achieve some progress on the 3</span><i><i><span style="font-family:Verdana;">x</span></i><span style="font-family:Verdana;"></span></i><span style="font-family:Verdana;"> + 1 problem. In particular, the</span> long<span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;">standing conjecture that nontrivial cycles do not exist is virtually proved using probability theory.</span></span>
文摘The author makes the claim to have a solution for the famous 3x + 1 problem. The key to its solution is a special proof that the term (3 + ε)<sup>r</sup> is a non-integer, as well as the use of properties of extremal points of a Collatz sequence.
