Boolean Hypercubes, Mersenne Numbers, and the Collatz Conjecture
نویسندگان
چکیده
منابع مشابه
Collatz Conjecture
My math 301 Term paper will be concerned with exploring the Collatz conjecture. I will discuss the importance and interest of this conjecture; what progress has been made on this problem and who made it. I will also explore whether any connections have been made between the Collatz conjecture and other mathematical problems.
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The first seventeen even perfect numbers are therefore obtained by substituting these values of ra in the expression 2n_1(2n —1). The first twelve of the Mersenne primes have been known since 1914; the twelfth, 2127 —1, was indeed found by Lucas as early as 1876, and for the next seventy-five years was the largest known prime. More details on the history of the Mersenne numbers may be found in ...
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Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography. Their form is such that modular reduction is extremely efficient, thus making them an attractive choice for modular multiplication implementation. However, the issue of residue multiplication efficiency seems to have been overlooked....
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We study variants of the well-known Collatz graph, by considering the action of the 3n+ 1 function on congruence classes. For moduli equal to powers of 2, these graphs are shown to be isomorphic to binary De Bruijn graphs. Unlike the Collatz graph, these graphs are very structured, and have several interesting properties. We then look at a natural generalization of these finite graphs to the 2-...
متن کاملThe Collatz 3n+1 Conjecture Is Unprovable
In this paper, we show that any proof of the Collatz 3n + 1 Conjecture must have an infinite number of lines. Therefore, no formal proof is possible. We also discuss whether the proof strategy in this paper has any promise for proving that the Riemann Hypothesis is also unprovable.
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ژورنال
عنوان ژورنال: Journal of Mathematical Sciences and Modelling
سال: 2020
ISSN: 2636-8692
DOI: 10.33187/jmsm.776898