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The phenomenon that π 4,3 (x) is ahead most of the time is called Chebyshev's bias. The prime number race generalizes to other moduli and is the subject of much research; Pál Turán asked whether it is always the case that π(x;a,c) and π(x;b,c) change places when a and b are coprime to c. [33] Granville and Martin give a thorough exposition ...
One record from this search is that 3 325 581 707 333 960 528 is the smallest number that cannot be written as a sum of two primes where one is smaller than 9781. [25] Cully-Hugill and Dudek prove [26] a (partial and conditional) result on the Riemann hypothesis: there exists a sum of two odd primes in the interval (x, x + 9696 log^2 x] for all ...
List of mathematical series. This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. is a Bernoulli polynomial. is an Euler number. is the Riemann zeta function. is the gamma function. is a polygamma function. is a polylogarithm.
Equivalently, The equation. A x + B y = C z {\displaystyle A^ {x}+B^ {y}=C^ {z}} has no solutions in positive integers and pairwise coprime integers A, B, C if x, y, z ≥ 3. The conjecture was formulated in 1993 by Andrew Beal, a banker and amateur mathematician, while investigating generalizations of Fermat's Last Theorem. [1][2] Since 1997 ...
Common cause. Treatment options. Brittle nails. Frequent wetting and drying. Apply lotions containing alpha hydroxy acids or lanolin. Soft or weak nails. Overexposure to moisture or chemicals ...
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, it is possible to expand the polynomial (x + y) n into a sum involving terms of the form ax b y c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending ...
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Zeckendorf's theorem. The first 89 natural numbers in Zeckendorf form. Each rectangle has a Fibonacci number Fj as width (blue number in the center) and Fj−1 as height. The vertical bands have width 10. In mathematics, Zeckendorf's theorem, named after Belgian amateur mathematician Edouard Zeckendorf, is a theorem about the representation of ...