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## 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...

## Coloring problems: ISI MMA 2018 Question 10

Understand the problem A new flag of ISI club is to be designed with 5 vertical strips using some or all the four colours : green , naroon , red and yellow . In how many ways this can be done  so that no two adjacent strips have the same colour ?  Source of the...

## Repunits in arbitrary bases

Understand the problem find all integers  such us  is a perfect square. Source of the problem New Zealand team training 2004 Topic Number Theory Difficulty Level Medium Suggested Book An Excursion in Mathematics Start with hints Hint 0Hint 1Hint 2Hint 3Hint 4 Do you...

## Argentina TST 2005

Understand the problem Let  and  be positive integers greater than , with  being a prime. Show that if  divides  and  divides , then  is a perfect square. Source of the problem Argentina TST 2005 Topic Number Theory Difficulty Level Easy Suggested Book An Excursion in...