From: John Robertson Subject: Re: Help me:form of ax^2+bx+c,if it=square of int for int x Date: Tue, 19 Dec 2000 04:09:04 GMT Newsgroups: sci.math Summary: [missing] In article <4yuh9tfj7529@forum.mathforum.com>, bacheli@hotmail.com (Eli) wrote: > I couldn't solve such problem ,which looks very simple: > f(x)=ax^2+bx+c is square of integer for every integer x. > Proove: f(x)=(cx+d)^2 for some integer c,d. Ed Barbeau, in his book Polynomials, Springer-Verlag, NY, 1989, discusses this problem on pages 398 and 399. He does not give a solution, but gives as a reference problem E869 in the American Mathematical Monthly, Vol 56, 1949, page 338, and Vol 57, 1950, page 114 to 116. This last gives a history of the problem, which apparently first appeared in 1894. Barbeau also references problems 114 and 190 on pages 132, 143, 325, and 341 of Polya and Szego, Problems and Theorems in Analysis, 4th edition, Springer. John Robertson Sent via Deja.com http://www.deja.com/