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Collatz Conjectures Proof by Number Theory |
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PP: 1-8 |
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doi:10.18576/sjm/120101
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Author(s) |
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Fereshteh Fazeli,
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Abstract |
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| In this paper, I discuss about different features of numbers, and with these features and using of powers of numbers (2)
and (3) with a new method in number theory, I prove that the Collatz conjecture is true for all numbers. Collatz conjecture was
proposed by Lothar Collatz in 1937. The famous mathematician Paul Erdos said about the Collatz conjecture, “Mathematics may not
be ready for such problems.“ Despite several efforts in this field, This dangerous problem remains unsolved. Unfortunately, there are
no mathematical models and formulas for the Collatz conjecture that I can use to prove this problem. Therefore, The scope of my
study in this field has been limited. So I prove this conjecture with my own achievements all along this article. In this paper, I prove
the accuracy of this conjecture with a new approach to number theory. Categorize numbers in groups and using different and beautiful
features in numbers, Finding a location of the next numbers which are constructed by odd numbers, Using powers of the number (2) and
number (3) as the foundation of my work, New method to show the same cycle of numbers in this problem, I introduce and innovative
method and distinct functionality to demonstrate this conjecture. Proof of the Collatz conjecture and several achievements in this article,
Definitely help mathematicians to work on other problems such as prime numbers, The Riemann hypothesis, The Goldbachs conjecture
in math, And some problems in astronomy which can be solved by the Collatz conjecture. These aspects set this article apart from
others. |
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