tag:blogger.com,1999:blog-3722233.post6040846843118046934..comments2023-03-25T10:00:22.914-05:00Comments on Computational Complexity: The key to my Taylor series problem: Buddy can you spare a penny, nickel, dime, or quarterLance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-3722233.post-7934293289347370472021-03-29T07:52:17.801-05:002021-03-29T07:52:17.801-05:00Are Putnam Problems meant to demonstrate encyclope...Are Putnam Problems meant to demonstrate encyclopedic knowledge of trick problems and the ability to apply them inside a weird math problem?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-78992242120897555062021-03-29T00:50:06.502-05:002021-03-29T00:50:06.502-05:00The money changing problem is problem No. 1 in the...The money changing problem is problem No. 1 in the classic Pólya, George; Szegő, Gábor (1972) [1925], Problems and theorems in analysis, 2 Vols, Springer-Verlag.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-83804057309371299692021-03-26T16:50:15.854-05:002021-03-26T16:50:15.854-05:00If you write the polynomial as (1 – x)(1 – x^5)(1 ...If you write the polynomial as (1 – x)(1 – x^5)(1 – x^10)(1 – x^25) then this is a well-known problem; see for example Chapter 1 of Donald J. Newman's book <i>Analytic Number Theory</i>. If it were a Putnam problem then a good solver would reason as follows: "This type of problem is difficult to do by hand in general, but this is the Putnam, so there has to be a slick solution. So the given expression must be a nice polynomial in disguise. Let's try to factor it."Timothy Chowhttp://alum.mit.edu/www/tchownoreply@blogger.com