User jeffrey shallit - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T00:30:03Z http://mathoverflow.net/feeds/user/10651 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/110239/is-there-an-algorithm-for-writing-a-number-as-a-sum-of-three-squares/110278#110278 Answer by Jeffrey Shallit for Is there an algorithm for writing a number as a sum of three squares? Jeffrey Shallit 2012-10-21T23:29:24Z 2012-10-21T23:54:46Z <p>This problem is discussed in my paper with Rabin, Randomized algorithms in number theory, Commun. Pure Appl. Math. 39, 1985, S239 - S256. We give an algorithm that, assuming a couple of reasonable conjectures, will produce a representation as a sum of three squares in random polynomial time.</p> http://mathoverflow.net/questions/104322/efficient-computation-of-integer-representation-as-sum-of-three-squares/110277#110277 Answer by Jeffrey Shallit for Efficient computation of integer representation as sum of three squares Jeffrey Shallit 2012-10-21T23:28:40Z 2012-10-21T23:28:40Z <p>This problem is discussed in my paper with Rabin, Randomized algorithms in number theory, Commun. Pure Appl. Math. 39, 1985, S239 - S256. We give an algorithm that, assuming a couple of reasonable conjectures, will produce a representation as a sum of three squares in polynomial time.</p> http://mathoverflow.net/questions/106313/algorithm-for-detecting-prime-powers/107031#107031 Answer by Jeffrey Shallit for Algorithm for detecting prime powers Jeffrey Shallit 2012-09-12T17:02:39Z 2012-09-12T17:02:39Z <p>See Dan Bernstein's paper, ``Detecting perfect powers in essentially linear time.'' Mathematics of Computation 67 (1998), 1253--1283, available at <a href="http://cr.yp.to/papers.html#powers" rel="nofollow">http://cr.yp.to/papers.html#powers</a>. Here "linear" means "linear in log n".</p> http://mathoverflow.net/questions/89600/numbers-with-known-irrationality-measures/91245#91245 Answer by Jeffrey Shallit for Numbers with known irrationality measures? Jeffrey Shallit 2012-03-15T03:54:15Z 2012-03-15T03:54:15Z <p>Yes, there are uncountably many "explicit" real numbers that are (i) badly approximable and (ii) transcendental and (iii) have easy-to-write-down binary expansions. See my paper with van der Poorten, Folded Continued Fractions, J. Number Theory 40 (1992), 237-250. I'm surprised Gerry Myerson didn't remember that!</p> http://mathoverflow.net/questions/24132/what-are-examples-of-mathematical-concepts-named-after-the-wrong-people-stigler/45248#45248 Answer by Jeffrey Shallit for What are examples of mathematical concepts named after the wrong people? (Stigler's law) Jeffrey Shallit 2010-11-08T01:57:28Z 2010-11-08T01:57:28Z <p>Farey series, attributed to Farey, were actually first studied by Haros. </p> http://mathoverflow.net/questions/110239/is-there-an-algorithm-for-writing-a-number-as-a-sum-of-three-squares/110278#110278 Comment by Jeffrey Shallit Jeffrey Shallit 2012-10-23T13:20:21Z 2012-10-23T13:20:21Z Yes, it works very quickly. http://mathoverflow.net/questions/101644/fiction-books-about-mathematicians/101668#101668 Comment by Jeffrey Shallit Jeffrey Shallit 2012-08-28T21:40:58Z 2012-08-28T21:40:58Z I do not recommend &quot;The Indian Clerk&quot; at all. The author seems to not understand much about mathematics, and it focuses much more on imagining what Hardy's homosexuality would have been like than on Ramanjuan (the &quot;Indian Clerk&quot; of the title) or mathematics.