tag:blogger.com,1999:blog-3722233.post127536327837647663..comments2022-01-27T21:41:51.434-06:00Comments on Computational Complexity: Ronald Graham: A summary of blog Posts We had about his workLance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-3722233.post-35656801575860188592020-07-15T07:40:44.380-05:002020-07-15T07:40:44.380-05:00Comment to item 2): This is still open, although t...Comment to item 2): This is still open, although the numbers are much smaller now.<br /><br />I believe the most recent pair was found in 2004: https://cs.uwaterloo.ca/journals/JIS/VOL7/Vsemirnov/vsem5.pdf<br />Johnhttps://www.blogger.com/profile/04086763657980407759noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-184192778955352592020-07-13T06:58:10.833-05:002020-07-13T06:58:10.833-05:00Comment to item 3):
A variant of this result showe...Comment to item 3):<br />A variant of this result showed up as problem 3 on the USA mathematical olympiad in 1978 (USAMO 1978):<br /><br />An integer n will be called good if we can write<br />n = a_1+a_2+...+a_k, where a_1,a_2,...,a_k are <br />positive integers (not necessarily distinct) satisfying<br />1/a_1 + 1/a_2 + ... + 1/a_k = 1.<br />Given the information that the integers 33 through 73 are <br />good, prove that every integer n>=33 is good. <br /><br />https://artofproblemsolving.com/wiki/index.php/1978_USAMO_ProblemsAnonymousnoreply@blogger.com