Four Squares Theorem

Introduction for four squares theorem:

Generally four squares theorems is the one of the important theorems in mathematics subject. These four squares theorem are classified into two types. They are Jacobi’s four square theorems and Lagrange’s four square theorems.  Now in this article we are going to discuss and explain about one of  these four squares theorem and its proof. Please express your views of this topic Area of Hexagonal Prism by commenting on blog.

Explanations for the Four Squares Theorem:

Here we have to explain for the both two four squares theorems.

Lagrange's four squares theorem:

It is simply states that, every positive integer has a demonstration (represent) as the sum of four squares values.

Jacobi’s four squares theorem:

We give a outline of Jacobi's four square theorem verification (proof) that the so many ways in which a positive integer can be written as a sum of four squares is the same to eight times the sum of those divisors which are not dividable by four

An accurate formula for the whole number of way for known positive integer ‘n’ can be represent as the sum (addition) of four squares. Is this topic A Triangle with One Obtuse Angle hard for you? Watch out for my coming posts.

Lagrange’s Four Squares Theorem:
Theorem statement:

All the (every) positive integers have representing the sum of four squares.

So that the natural numbers be capable of be represented as the sum of four squares by the way of,

Four square theorem proof:

`P = x_0^2 + x_1^2 +x_2^2 + x_3^2`

Here, the four numbers x1, x2, x3, x4 are integers.

This is the important in Lagrange’s four squares theorem.

For example illustration (representation) for `3, 41, 210`

Examples:

`3 = 1^2 + 1^2 + 1^2 + 0^2`
`41 = 6^2 + 2^2 + 1^2 + 0^2`
`210 = 14^2 + 3^2 + 2^2 + 1^2.`
Example practices using Lagrange’s theorems:

Examples: 100, 118, and 5.

Answers:    ` 100 = 5^2 +5^2 + 5^2 +5^2`

` 118 = 10^2 + 4^2 + 1^2 +1^2`

` 5 = 2^2 + 1^2 + 0^2 + 0^2`

Those all above explanations and examples will clear the four squares theorems.