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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We use the previously known value for for S q 5 and solve for S q to obtain a value for.

An unelegant solution to the described problem which works in principle: Truly Ramanujan is the Mozart of Mathematics. Or continue as a guest your comment will be held for moderation:. These functions are related by. Several of the problems are elementary and can be attacked with a background of only high school mathematics.

An elementary solution to the specific geometric problem you’ve mentioned can be found in Ramanujan’s Notebooks, Part III by Berndt Springer,pp. Oh well, he sure can make us rack our brains out.

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Name Please enter your name. Doing a few numerical examples proves then that there is at least a large enough set of real solutions. This survey is available from Bruce Berndt website: Rmanujan problem stems from Ramanujan’s pgoblems on modular equations of degree Why can’t you this as a separate question?

Email Please enter a valid email address. In the Wikipedia page on Ramanujan, there is a link to a collection of problems posed ramanjan him. So, Are all these problems solved? Koundinya Vajjha 1 14 Thank you for the link. As one can see, the Roger—Ramanujan functions are beautiful, not just due to their mathematical properties, but also visually.

An actual proof can be accomplished using modular equations. A result of Siegel implies that the number of solutions in each case is finite.

## After 100 Years, Ramanujan Gap Filled

The geometric version of continued fractions is known as the Rogers—Ramanujan function R. Would you like to answer one of these unanswered questions instead? The solution is given in the second link in pp. I just cannot resist posting it here! For each type, we can predict behaviors with such things as partial sum formulas.

This is of course ugly but has the advantage that you can give the heavy work to a machine. The presence of the prefactor makes various formulas nicer. The page has a collection of about sixty problems which have appeared in the Journal of the Indian Mathematical Society.

## Ramanujan–Nagell equation

Why were the problems posed exactly? More formal definitions are as follows: The values of n correspond to the values of x as: More formal definitions are as follows:. Thank you for your interest in this question.

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. All he had was a pen and pad of paper no Mathematica at that timeand he wanted to write down his equations before he died.

Roland Bacher 6, 26 For others, significant amounts of hard analysis are necessary to effect solutions, and a few problems have not been completely solved. A century ago, Srinivasa Ramanujan and G. Views Read Edit View history. Within months, he passed away, probably from hepatic amoebiasis. We start by comparing arithmetic sequences to geometric sequences.

It is named after Srinivasa Ramanujanwho conjectured that it has only five integer solutions, and after Trygve Nagellwho proved the conjecture.

### Ramanujan–Nagell equation – Wikipedia

The values agree to at least places. Since both of these are algebraic numbers with elegant representations, this is a rather convincing check. Older Gigapixel Images in Mathematica. That line at the end is equivalent to. He claimed to have solutions for a particular function, but only had time to unslved down a few before moving on to other areas of mathematics.

By using this site, you agree to the Terms of Use and Privacy Policy. In Ramanujan was deathly ill while on a long ride back to India, from February 27 to March 13 on the steamship Nagoya.

Second, conjecture a closed algebraic form for this number. This is named after M. Hardy, who in turn gave it to mathematician G.