SOME MORE CONJECTURES ON PRIMES AND DIVISORS

There are an innumerable numbers of conjectures and unsolved problems in number theory predominantly on primes which have been giving sleepless nights to the mathematicians allover the world for centuries

DEFINITIONS, SOLVED AND UNSOLVED PROBLEMS, CONJECTURES, AND THEOREMS IN NUMBER THEORY AND GEOMETRY

Florentin Smarandache, an American mathematician of Romanian descent has generated a vast variety of mathematical problems. Some problems are easy, others medium, but many are interesting or unsolved and this is the reason why the present book appears. Here, of course, there are problems from various types. Solving these problems is addictive like eating pumpkin seed: having once started, one cannot help doing it over and over again

Erdos Conjecture I.

In this short paper I show how it is related to other famous unsolved problems in prime number theory. In order to do this, I formulate the main hypothetical result of this paper - a useful upper bound conjecture (Conjecture 3.), describing one aspect of the distribution of primes in various special forms, paying a brief attention to Fermat, Mersenne, Fibonacci, Lucas and Smarandache sequences, and I debate some side effects of the most surprising results it implies. At the end I also give connections of the questions discussed to other important areas of prime number theory, such as topics from the theory of distribution of primes in denser sequences, and along the way I mention some further conjectures of Erdos that have relevant applications there

An Infinity Of Unsolved Problems Concerning A Function In The Number Theory

W.Sierpinski has asserted to an international conference that if mankind lasted for ever and numbered the unsolved problems, then in the long run all these unsolved problems would be solved

On the Uniformity of (3/2)n(3/2)^n Modulo 1

It has been conjectured that the sequence $(3/2)^n$ modulo $1$ is uniformly distributed. The distribution of this sequence is signifcant in relation to unsolved problems in number theory including the Collatz conjecture. In this paper, we describe an algorithm to compute $(3/2)^n$ modulo $1$ to $n = 10^8$. We then statistically analyze its distribution. Our results strongly agree with the hypothesis that $(3/2)^n$ modulo 1 is uniformly distributed.Comment: 12 pages, 2 figure

Funny Problems!

Thirty original and collected problems, puzzles, and paradoxes in mathematics and physics are explained in this paper, taught by the author to the elementary and high school teachers at the University of New Mexico - Gallup in 1997-8 and afterwards. They have more an educational interest, because make the students think different! For each "solution" a funny logic is invented in order to give the problem a sense.Comment: 6 pages. Part of a project with UNM-G students. Partially publisehd in "Definitions, Solved and Unsolved Problems, Conjectures, and Theorems in Number Theory and Geometry", edited by M. L. Perez, 86 p., Xiquan Publishing House, Phoenix, 200