Monthly Archives: December 2020

Proof: Quadratic Reciprocity Law

Posted on December 28, 2020 by Sumant Sumant
Posted in Abstract Algebra, Famous Problem, Number Theory, Proof, Proof by Construction | Tagged | Leave a comment

Proof: Why there are infinite number of 4k+1 Primes ?

Posted on December 27, 2020 by Sumant Sumant
Posted in Famous Problem, Modular Arithmetic, Number Theory, Proof, Proof by Construction | Tagged | Leave a comment

Proof: Equivalent condition for Gauss’s Lemma

Posted on December 27, 2020 by Sumant Sumant
Posted in lemma, Modular Arithmetic, Number Theory, Proof, Proof by Construction | Tagged | Leave a comment

Proof: Values of (2/p) using Gauss’s Lemma

Posted on December 26, 2020 by Sumant Sumant
Posted in Modular Arithmetic, Number Theory, Proof | Leave a comment

Any n lines are concurrent (Using Mathematical Induction)

Posted on December 26, 2020 by Sumant Sumant
Posted in Geometry, Mathematical Induction, Proof, Proof by Contradiction | Leave a comment

Applying Quadratic Reciprocity Law

Posted on December 26, 2020 by Sumant Sumant
Posted in Modular Arithmetic, Number Theory | Tagged | Leave a comment

Simultaneous Multiple Choice Linear Congruence Question 2

Posted on December 20, 2020 by Sumant Sumant

For which of the following 4-tuples of integers do we have a solution to the system of simultaneous linear congruences: The first thing to notice here is that we have three different mods however all three are not different as … Continue reading →

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Multiple Choice Simultaneous Linear Congruence Question 1

Posted on December 20, 2020 by Sumant Sumant

For which of the following 3-tuples of integers do we have a solution to the system of simultaneous linear congruences: The first thing to notice here is that we have three different mods however all three are not different as … Continue reading →

Posted in Number Theory | Tagged | Leave a comment

Proof: Gauss’s Lemma

Posted on December 18, 2020 by Sumant Sumant

The test is where is the number of terms that are bigger than which is always a decimal. After seeing Dirichlet theorem and Euler’s criteria. One appreciates the exponent . That gives us the hint of using only the first … Continue reading →

Posted in Number Theory, Proof, Proof by Construction, Proof by Contradiction | Leave a comment

Evaluating Legendre Symbol (3/7) by 4 different methods

Posted on December 17, 2020 by Sumant Sumant
Posted in Number Theory | Tagged | Leave a comment