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## 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...

## RMO 2019

RMO 2019 Regional Mathematics Olympiad, India 2019… welcome to the festival of mathematics  Tool box for Regional Math Olympiad 2019 Geometry Tools for RMO Read More Number Theory Tools for RMO Read More Combinatorics Tools for RMO Read More Algebra Tools for...

## Application of eigenvalue in degree 3 polynomial: ISI MMA 2018 Question 14

Understand the problem Let A be a 3 x 3 real matrix with all the diagoanl entries equal to 0 . If 1 + i is an eigen value of A , the determinant of A equal ? Source of the problem Sample Questions (MMA ) :2019 Topic Linear Algebra Difficulty Level Medium Suggested...

## To find Trace of a given Matrix : ISI MMA 2018 Question 13

Understand the problem If A = begin{bmatrix} 2&i\i&0end{bmatrix} , the trace of (A^{10}) is Source of the problem Sample Questions (MMA):2019 Topic Linear Algebra Difficulty Level Medium Suggested Book Introduction to Linear Algebra by Pearson Start with hints...

## Costa Rica NMO 2010, Final Round, Problem 4 – Number Theory

Understand the problem Find all integer solutions  of the equation Source of the problem Costa Rica NMO 2010 Topic Number Theory Difficulty Level 6/10 Suggested Book A Friendly Introduction to Number Theory by J.H.Silverman Start with hints Hint 0Hint 1Hint 2Hint...

## Problems on quadratic roots: ISI MMA 2018 Question 9

Understand the problem If  (alpha) is a root of  (x^2) – x +1 = 0 , then (alpha^{2018})  + (alpha^{-2018})  is  Source of the problem Sample Questions (MMA) : 2019 Topic Quadratic Roots Difficulty Level Medium  Suggested Book Abstract Algebra – Dummit and...