Fundamental Theorem of Algebra: Two Proofs

Introduction

Fundamental theorem of algebra is one of the most famous results provided in higher secondary courses of mathematics. Normally it is mentioned in chapter related to complex numbers where the reader is made aware of the power of complex numbers in solving polynomial equations. The theorem guarantees that any non-constant polynomial with real or complex coefficients has a complex root.

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Congruence Properties of Partitions: Part 2

Continuing our journey of partition congruences from the last post we now prove the congruences modulo $7$ and $11$.

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Congruence Properties of Partitions: Part 1

Introduction

We know that any positive integer greater than $1$ can be expressed as a product of prime numbers in a unique fashion ignoring the order of factors. This is one of the most basic results in number theory and is aptly called the fundamental theorem of arithmetic. This result also shows that prime numbers are the building blocks for all integers and this justifies the importance given to prime numbers in number theory.

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