Mathematical Circles Inequality Problem

Mathematical Circles Inequality Problem

Understand the problem If (a,b) are positive reals such that (a+b<2) ,then prove that  $$ displaystyle frac {1}{1+a^2} + frac {1}{1+b^2} leq frac {2}{1+ab} $$ Source of the problem Mathematical Circles Topic Inequality involving AM-GM Difficulty Level Medium...
AMC 2019 12A Problem 15 Diophantine Equation

AMC 2019 12A Problem 15 Diophantine Equation

Understand the problem Positive real numbers  and  have the property thatand all four terms on the left are positive integers, where log denotes the base 10 logarithm. What is ? Source of the problem 2019 AMC 12A Problems/Problem 15 Topic logarithm, diophantine...
2008 AMC 8 Problem 22 Number theory

2008 AMC 8 Problem 22 Number theory

                                    Understand the Problem For how many positive integer values of (n) are both ( frac {n}{3} ) and ( 3n ) three-digit whole numbers? Source of the problem 2008 AMC 8 Problem 22 Topic Number Theory Difficulty Level Easy Suggested Book...