MathDB

2

Part of 2017 China Second Round Olympiad

Problems(2)

China Second Round Olympiad 2017 Test 1 Q2

Source: Sep 10, 2017

9/10/2017
Let x,y x,y are real numbers such that x2+2cosy=1x^2+2cosy=1. Find the ranges of x−cosyx-cosy.
algebrainequalities
Sequence

Source: China Second Round 2017(A), Test 2, Problem 2

2/22/2018
Given a sequence {an}\{a_n\}: a_1=1, a_{n+1}=\left\{ \begin{array}{lcr} a_n+n,  a_n\le n, \\ a_n-n,  a_n>n, \end{array} \right.   n=1,2,\cdots. Find the number of positive integers rr satisfying ar<r≤32017a_r<r\le 3^{2017}.
algebraSequence