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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A tout seigneur tout honneur!

This is of course ugly but has the advantage that you can give the heavy work to a machine. The values agree to at least places. You may want to see this paper as well by Berndt: We do not record the value here, because it is not particularly elegant. So how did Ramanujan come up with such a problem? Or continue as a guest your comment will be held for moderation: Ramanujan used chalk and his mind to simplify most of his results—the long results he erased from his slate, but the elegant results he wrote down.

Retrieved from ” https: Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site the association bonus does not count.

That line at the end is equivalent to. An elementary solution to the specific geometric problem you’ve ra,anujan can be found in Ramanujan’s Notebooks, Part III by Berndt Springer, unsolvedd, pp. An actual proof can be accomplished using modular equations. Since both of these are algebraic numbers with elegant representations, this is a rather convincing check.

Tamanujan Science Technology-enabling science of the computational universe. Andrey Rekalo 19k 9 72 This is named after M. Why can’t you this as a separate question? Five years and a day later, he became a Fellow of the Royal Society, then the most prestigious scientific group in the world at that time.

Why were the problems posed exactly? This page was last edited on 20 Juneat Legal Site Map WolframAlpha.

For each type, we can predict behaviors with such things as partial sum formulas. The intuition behind the problem will be more interesting if it is known. Thank you for the link.

In mathematicsin the field of number theorythe Ramanujan—Nagell equation is an equation between a square number and a number that is seven less than a power of two. Views Read Edit View porblems. There is a survey article by Berndt, Choi, and Kang devoted to the set of 58 Ramanujan’s problems.

I just cannot resist posting it here! His final notebook was sent by the University of Madras to G. Second, conjecture a closed algebraic form for this number.

### theory – The Ramanujan Problems. – MathOverflow

Ramaunjan solution is given in the second link in pp. Wolfram Universal Deployment System Instant deployment across cloud, desktop, mobile, and more. The values of n correspond to the values of x as: In Ramanujan was deathly ill while on a long ride back to India, from February 27 to March 13 on the steamship Nagoya.

Thank you for your interest in this question.

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Within months, he passed away, probably from hepatic amoebiasis. MathOverflow works best with JavaScript enabled. Computational Exploration in the Wolfram Language August 2, Hardy, who in turn gave it to mathematician G. From Wikipedia, the free encyclopedia. FYI, your link does not work without an account on Google docs or something like this.

## Ramanujan–Nagell equation

It is named after Unsilved Ramanujanwho conjectured that it has only five integer solutions, and after Trygve Nagellwho proved the conjecture. This is probles modular equation of order 5 for S: This problem is mentioned in the link provided in Andrey Rekalo’s answer below in pp.

For others, significant amounts of hard analysis are necessary to effect solutions, and a few problems have not been completely solved. Roland Bacher 6, 26 Many of these have been found since Ramanujan wrote them down. Posted by Victor T. They indicate that the questions had originally appeared in the problems section of the Journal and apparently the editors published readers’ solutions in subsequent issues.

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