一、试题原文1. For each integer n > 1, let p(n) denote the largest prime factor of n. Determine all triples x,y,z of distinct positive integers satisfying(i) x,y,z are in arithmetic progression and(ii) p(xyz)≤3.2....一、试题原文1. For each integer n > 1, let p(n) denote the largest prime factor of n. Determine all triples x,y,z of distinct positive integers satisfying(i) x,y,z are in arithmetic progression and(ii) p(xyz)≤3.2. Let ABC be a triangle and let D be a point on AB such that 4AD = AB. The half - line l is drawn on the same side of AB as C, starting from D and making an angle of θwith DA where θ=∠ACB. If展开更多
1.Consider a standard twelve-hour Clock whosehour and minute hands move continuously.Let m be aninteger,with 1≤m≤720.At precisely m minutesafter 12:00,the angle made by the hour hand andminute hand is exactly 1°...1.Consider a standard twelve-hour Clock whosehour and minute hands move continuously.Let m be aninteger,with 1≤m≤720.At precisely m minutesafter 12:00,the angle made by the hour hand andminute hand is exactly 1°.Determine all possible valuesof m.2.Find the last three digits of the number2003 2002 2001。3.Find all real positive solutions(if any)tOx3+y3+z3=x+y+z,andx2+y2+z2=xyz.展开更多
文摘一、试题原文1. For each integer n > 1, let p(n) denote the largest prime factor of n. Determine all triples x,y,z of distinct positive integers satisfying(i) x,y,z are in arithmetic progression and(ii) p(xyz)≤3.2. Let ABC be a triangle and let D be a point on AB such that 4AD = AB. The half - line l is drawn on the same side of AB as C, starting from D and making an angle of θwith DA where θ=∠ACB. If
文摘1.Consider a standard twelve-hour Clock whosehour and minute hands move continuously.Let m be aninteger,with 1≤m≤720.At precisely m minutesafter 12:00,the angle made by the hour hand andminute hand is exactly 1°.Determine all possible valuesof m.2.Find the last three digits of the number2003 2002 2001。3.Find all real positive solutions(if any)tOx3+y3+z3=x+y+z,andx2+y2+z2=xyz.
