原文地址:2014美国数学奥林匹克不等式题及其证明作者:sqing55 已知 ,求证: 证明(n mbersandn mbers):, so . expanding yields .therefore and ,, so it is always positive. dividing by yields similarly, the same is tr e for and . m ltiplying the expressions for , , and yields . since all q antities are positive , one of , , or m st be . in other words, .is there s ch thing as a cyclic prod ct? i ve never seen one sed. 2014 brazilian olympic revenge 已知 是正整数. 证明: . 证明有无穷多个满足不等式 的正整数 .