Did you get that from Recreative Algebra by Yakov Isidorovich Perelman? His books are full of wonderful problems like this one. On 12/31/17 18:14 , James Propp wrote:
Here's a (somewhat late) Diophantine puzzle in honor of the 365th day of the year:
It is not hard to show that 365 can be written as both 10^2 + 11^2 + 12^2 and 13^2 + 14^2. (This fact came to my attention about twenty years ago through Nikolai Petrovich Bogdanov-Belsky's painting "Mental Calculation in the Public School Of S. A. Rachinsky", which you can view at https://goo.gl/images/yo88LY.
Puzzle: Show that there are infinitely many integers that can be written both as a sum of two consecutive squares and as a sum of three consecutive squares.
For extra credit, find the proof mentally. :-)
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun .