Monthly Archives: October 2010

Quadratic Residues – I

Definition. For and , Then , we define say that is residue of nth-degree modulo m , If there exist integer solutions for –   Otherwise, It is non-residue of nth-degree modulo m. For we call it as quadratic, cubic and bi-quadratic residues respectively. Theorem : There are quadratic residues in . Proof : Consider […]

Awed ..

And miles to go before i sleep, And miles to go before i sleep … .. .. ..

Some Standout methods of approach

The Area Way Incases , where a relation with areas is possible, It is quite efficient to use it to solve the problem. Example – If are the altitudes of a triangle from A,B,C to the opposite sides and r is the inradius. Prove that – 1. 2. Proof Let I be the incentre. Note […]

Basic Insights on Geometrical Inequalities.

With the on-going trend, Algebraic Inequalities are almost erasing the existence of Geometrical Inequalities . Nevertheless, They are equally beautiful (if not more) , although they seem a lot harder to me. Yes, they can mostly be proved by brute-force trigononmetry or complex (whatever it is , they are equally good solutions) , but I […]