Mahavira's Contributions to Number Theory

Mahavira's Theorem states that every positive integer can be expressed as the sum of three prime numbers. This theorem was first stated by Mahavira in his book Ganita Sara Samgraha.

Euclid's Theorem states that there are infinitely many prime numbers. This theorem was first stated by Euclid in his book Elements.

Legendre's Theorem states that the sum of two squares can never be a prime number. This theorem was first stated by Adrien-Marie Legendre in his book Théorie des Nombres.

Mersenne's Theorem states that every even perfect number is of the form $2^{p-1}(2^p - 1)$, where $p$ is a prime number. This theorem was first stated by Marin Mersenne in his book Cogitata Physico-Mathematica.

Euler's Theorem states that every odd perfect number is of the form $p^a q^b r^c ...$, where $p$, $q$, $r$, ... are distinct prime numbers and $a$, $b$, $c$, ... are positive integers. This theorem was first stated by Leonhard Euler in his book Introductio in Analysin infinitorum.

Euler's Theorem states that the number of divisors of a positive integer $n$ is equal to the product of the exponents of the prime factors of $n$ plus one. This theorem was first stated by Leonhard Euler in his book Introductio in Analysin infinitorum.

Euclid's Theorem states that the sum of the divisors of a positive integer $n$ is equal to the product of the factors of $n$. This theorem was first stated by Euclid in his book Elements.

Euclid's Theorem states that the product of two consecutive integers is always odd. This theorem was first stated by Euclid in his book Elements.

Euclid's Theorem states that the sum of the squares of the first $n$ positive integers is equal to $rac{n(n+1)(2n+1)}{6}$. This theorem was first stated by Euclid in his book Elements.

Euclid's Theorem states that the sum of the cubes of the first $n$ positive integers is equal to $rac{n^2(n+1)^2}{4}$. This theorem was first stated by Euclid in his book Elements.

Euclid's Theorem states that the sum of the fourth powers of the first $n$ positive integers is equal to $rac{n(n+1)(2n+1)(3n^2+3n-1)}{30}$. This theorem was first stated by Euclid in his book Elements.

Euclid's Theorem states that the sum of the fifth powers of the first $n$ positive integers is equal to $rac{n^2(n+1)^2(2n^2+2n-1)}{12}$. This theorem was first stated by Euclid in his book Elements.

Euclid's Theorem states that the sum of the sixth powers of the first $n$ positive integers is equal to $rac{n(n+1)(2n+1)(3n^3+3n^2-n-1)}{42}$. This theorem was first stated by Euclid in his book Elements.

Euclid's Theorem states that the sum of the seventh powers of the first $n$ positive integers is equal to $rac{n^3(n+1)^3}{8}$. This theorem was first stated by Euclid in his book Elements.

Euclid's Theorem states that the sum of the eighth powers of the first $n$ positive integers is equal to $rac{n(n+1)(2n+1)(3n^4+6n^3-3n^2+2n-1)}{30}$. This theorem was first stated by Euclid in his book Elements.