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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
The conjecture is that there is a simple way to tell whether such equations have a finite or infinite number of rational solutions. More specifically, the Millennium Prize version of the conjecture is that, if the elliptic curve E has rank r , then the L -function L ( E , s ) associated with it vanishes to order r at s = 1 .
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
Fermat's Last Theorem considers solutions to the Fermat equation: a n + b n = c n with positive integers a, b, and c and an integer n greater than 2. There are several generalizations of the Fermat equation to more general equations that allow the exponent n to be a negative integer or rational, or to consider three different exponents.
In new research, mathematicians have narrowed down one of the biggest outstanding problems in math. Skip to main content. 24/7 Help. For premium support please call: 800-290-4726 more ways to ...
For example, for 2 5 a + 1 there are 3 increases as 1 iterates to 2, 1, 2, 1, and finally to 2 so the result is 3 3 a + 2; for 2 2 a + 1 there is only 1 increase as 1 rises to 2 and falls to 1 so the result is 3a + 1. When b is 2 k − 1 then there will be k rises and the result will be 3 k a + 3 k − 1.
The value ζ(0) = −1/2 is not determined by the functional equation, but is the limiting value of ζ(s) as s approaches zero. The functional equation also implies that the zeta function has no zeros with negative real part other than the trivial zeros, so all nontrivial zeros lie in the critical strip where s has real part between 0 and 1.
⋮ g 1 = n th tower: 3↑3↑3↑3↑3↑3↑3↑...↑3 (number of 3s is given by the n − 1 th tower) where the number of 3s in each successive tower is given by the tower just before it. The result of calculating the third tower is the value of n , the number of towers for g 1 .
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