21 Dec Unsolved problems in Number Theory and Prizes. DISCUSSION BETWEEN HARDY AND LITTLEWOOD. Hardy shows the letter of Ramanujan. There is a survey article by Berndt, Choi, and Kang devoted to the set of 58 Ramanujan’s problems. They indicate that the questions had. In mathematics, in the field of number theory, the Ramanujan–Nagell equation is an equation Triangular Mersenne numbers[edit]. The problem of finding all numbers of the form 2b − 1 (Mersenne numbers) which are triangular is equivalent.

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In Ramanujan was deathly ill while on a long ride back unsolvd India, from February 27 to March 13 on the steamship Nagoya. Roland Bacher 6, 26 I originally thought of asking this question at the Mathematics Stackexchange, but then I decided that I’d have a better chance of a good discussion here.

The presence of the prefactor makes various formulas nicer. Views Read Edit View history.

Ramanujan–Nagell equation

Another form of arithmetic progression, in the realm of continued fractionsis the following:. This is the modular equation of order 5 for S:. For each type, we can predict behaviors with such things as partial sum formulas.


First, calculate a numerical value for the point of interest. Big O and Friends: He wrote the following incomplete equation with 14 others, only 3 of them solved.

After 100 Years, Ramanujan Gap Filled

It is named after Srinivasa Ramanujanwho conjectured that it has only five integer solutions, and after Trygve Nagellwho proved the conjecture. This problem is mentioned in the link provided in Andrey Rekalo’s answer below in pp. Here is one problem from the list. With SimplifyUbsolvedand many other Mathematica functions, large equations can ;roblems boiled down to their most elegant form. Many of these have been found since Ramanujan wrote them down.

After Years, Ramanujan Gap Filled—Wolfram Blog

This survey is ramwnujan from Bruce Berndt website: Is’nt this the approach of Wu to solve geometric problems by mechanical methods? From Wikipedia, the free encyclopedia. Retrieved from ” https: Values returned can be complex, so these pictures show the imaginary, real, argument, and absolute values Im, Re, Arg, and Abs of the function R q. Thank you for your interest in this question.


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These functions are related by. Diophantine equations Srinivasa Ramanujan. Computational Exploration in the Wolfram Language August 2, Oh well, he sure can make us rack our brains out. The values of rwmanujan correspond to the values of x as: Or are there more ramanuhan problems among them?

Then we check that the numerical value of the conjectured form is the same as the value of the function. MathOverflow works best with JavaScript enabled.

We start by comparing arithmetic sequences to geometric sequences. Several of the problems are elementary and can be attacked with a background of only high school mathematics. Here are pictures of the behavior of usolved R function on the unit disk in the complex plane.

This is named after M. Finally, check the conjectured form with many digits of accuracy.