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## Geometry of AM GM Inequality

Get motivated… try this quiz Understand the problem Arithmetic mean and Geometric mean are useful algebraic tools. They have beautiful geometric interpretation as well. The following video takes a tour into the ideas. Tutorial Problems… try these before...

## Geometry of Cauchy Schwarz Inequality

Understand the problem Cauchy Schwarz Inequality is a powerful tool in Algebra. It was beautiful geometric implications as well. Watch the video and solve the tutorial problems to delve deep into the idea. Tutorial Problems! 1. Look at the expression ( sqrt{x_1^2 +...

## RMO 2019 Maharashtra and Goa Problem 2 Geometry

Understand the problem Given a circle , let be a point in its interior, and let be a line passing through .  Construct with proof using a ruler and compass, all circles which pass through , are tangent to , and whose centres lie on . Source of the problem RMO 2019...

## RMO 2019 (Maharashtra Goa) Adding GCDs

Understand the problem For each ( n  in mathbb{N} ) let ( d_n ) denote the G.C.D. of n and (2019 – n). Find the value of (  d_1 +  d_2 + … + d_{2019} ). Source of the problem Regional Math Olympiad, 2019, Maharashtra, Goa Region Problem 1 Topic Number...

## Number Theory, Ireland MO 2018, Problem 9

Understand the problem The sequence of positive integers  satisfies  for .Prove that there exists at most one  for which  is the cube of an integer. Source of the problem Ireland MO 2018, Problem 9 Topic Number Theory Difficulty Level 8/10 Suggested Book Excursion in...

## Number Theory, France IMO TST 2012, Problem 3

Understand the problem Let  be a prime number. Find all positive integers  such that: Source of the problem France IMO TST 2012, Problem 3 Topic Number Theory Difficulty Level 7/10   Suggested Book Challenges and Thrills of Pre College Mathematics Start with...