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 23:01, 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
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.