Difference between revisions of "1994 USAMO Problems/Problem 1"
| Line 1: | Line 1: | ||
| + | Let <math> \, k_1 < k_2 < k_3 <\cdots\, </math>, be positive integers, no two consecutive, and let <math> \, s_m = k_1+k_2+\cdots+k_m\, </math>, for <math> \, m = 1,2,3,\ldots\;\; </math>. Prove that, for each positive integer <math>n</math>, the interval <math> \, [s_n, s_{n+1})\, </math>, contains at least one perfect square. | ||
| + | |||
==Solution== | ==Solution== | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 22:01, 22 May 2014
Let 
, be positive integers, no two consecutive, and let 
, for 
. Prove that, for each positive integer 
, the interval 
, contains at least one perfect square.
Solution
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
