# Category Algebra

## Interesting Egyptian Fraction Problem

Here is an interesting mathematical puzzle alike problem involving the use of Egyptian fractions, whose solution sufficiently uses the basic algebra. Problem Let a, b, c, d and e be five non-zero complex numbers, and; $a + b + c + d + e = -1$ … (i) $a^2+b^2+c^2+d^2+e^2=15$ …(ii) $\dfrac{1}{a} + \dfrac{1}{b} +\dfrac{1}{c} +\dfrac{1}{d} +\dfrac{1}{e}= -1$…

## Irrational Numbers and The Proofs of their Irrationality

“Irrational numbers are those real numbers which are not rational numbers!” Def.1: Rational Number A rational number is a real number which can be expressed in the form of where $a$ and $b$ are both integers relatively prime to each other and $b$ being non-zero. Following two statements are equivalent to the definition 1. 1. $x=\frac{a}{b}$…