Historically, it seems that the result was first discovered by Ramanujan, who described it in one of his letters to G. Hardy as "If I tell you this you will at once point out to me the lunatic asylum as my goal""If I tell you this you will at once point out to me the lunatic...
A Negative Number as Sum of All Natural Numbers: Between Culture and MathematicsIn remarkable books in Theoretical Physics and String Theory an indication appears that the sum of the natural numbers is equal to minus one divided by twelve. Over the Internet one can find a proof which uses, ...
So I've just been reading that the proof that sum of all natural numbers 1 + 2 + 3 + 4... = -1/12 the mathematical proof is sound but it causes some problems like: how come the sum of 2 natural numbers is a fraction??? my answer is because we aren't dealing with a natural...
not created: it has arisen little by little from a small beginning, and has increased through the activity of the elemental forces embodied in itself, and so has rather grown than come into being at an almighty word.”“What a sublime idea ...
In 1917, Hardy and Ramanujan proved that the n... Troupe,Lee - 《Journal of Number Theory》 被引量: 8发表: 2015年 An analogue in certain unique factorization domains of the Euclid-Euler theorem on perfect numbers We show that there exists a natural extention of the sum of divisors ...
We define a sum as a set x, y, z of distinct natural numbers such that x + y = z, and let Nm = 1, 2, . . . , m. We introduce a new sequence h(n) defined as the smallest s such that there is no partition of Ns into n sum-free parts. We determine h(n) for n = ...
recent results show that polynomial subsequences of automatic sequences, such as the Thue–Morse sequence, are better candidates for pseudorandom sequences. A natural generalization of automatic sequences are morphic sequences, given by a fixed point of a prolongeable morphism that is not necessaril...
J Li,J Ma - 《Journal of Number Theory》 被引量: 0发表: 2023年 On some sums involving the integral part function Denote by τ k (n) , ω (n) and μ 2 (n) the number of representations of n as a product of k natural numbers, the number of distinct prime factors of n an.....
J Liu,MC Liu - 《Journal of Number Theory》 被引量: 44发表: 2000年 On the Representation of Natural Numbers as Sums of Squares. Assessment of mathematicians; Theories made by mathematicians stating that every positive integer is the sum of the four squares of integers; Proof to ... Panai...
To successfully invade new hosts, plant viruses must break host resistance and be competent to move within and between plant cells. As a means, viral proteins known as pathogenicity determinants have evolved to coordinate a network of protein interaction