Lagrange Four Square Theorem (Bachet Conjecture) Calculator

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Lagrange Four Square Definition

For any natural number (p), we write as

p = a² + b² + c² + d²

Determine max_a:

Floor(√) = Floor()

Floor() = 0
This is called max_a

Determine min_a:

Find the first value of a such that
a² ≥ n/4

Start with min_a = 0 and increase by 1

Continue until we reach or breach n/4 → /4 = 0

When min_a = 0, then it is a² = 1 ≥ 0, so min_a = 0

Find a in the range of (min_a, max_a)

(0, 0)

a = 0

Find max_b which is Floor(√n - a²)

max_b = Floor(√ - 0²)

max_b = Floor(√ - 0)

max_b = Floor(√0)

max_b = Floor(0)

max_b = 0

Find b such that b² ≥ (n - a²)/3

Call it min_b

Find b

Start with min_b = 0 and increase by 1
Go until (n - a²)/3 → ( - 0²)/3 = 0

When min_b = 0, then it is b² = 1 ≥ 0, so min_b = 0

Test values for b in the range of (min_b, max_b)

(0, 0)

b = 0

Determine max_c =Floor(√n - a² - b²)

max_c = Floor(√ - 0² - 0²)

max_c = Floor(√ - 0 - 0)

max_c = Floor(√0)

max_c = Floor(0)

max_c = 0

Step 5b. Obtain the first value of b such that b² ≥ (n - a²)/3

Call it min_b

Start with min_c = 0 and increase by 1

Go until (n - a² - b² )/2 → ( - 0² - 0²)/2 = 0

When min_c = 0, then it is c² = 1 ≥ 0, so min_c = 0

c = 0

See if d is an integer solution which is √n - a² - b²

max_d = √ - 0² - 0² - 0²

max_d = √ - 0 - 0 - 0

max_d = √0

max_d = 0

Since max_d = 0, then (a, b, c, d) = (0, 0, 0, 0) is an integer solution proven below

0² + 0² + 0² + 0² → 0 + 0 + 0 + 0 =

List out 1 solutions:

(a, b, c, d) = (0, 0, 0, 0)

You have 1 free calculations remaining

What is the Answer?

(a, b, c, d) = (0, 0, 0, 0)

How does the Lagrange Four Square Theorem (Bachet Conjecture) Calculator work?

Free Lagrange Four Square Theorem (Bachet Conjecture) Calculator - Builds the Lagrange Theorem Notation (Bachet Conjecture) for any natural number using the Sum of four squares.
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What 1 formula is used for the Lagrange Four Square Theorem (Bachet Conjecture) Calculator?

What 7 concepts are covered in the Lagrange Four Square Theorem (Bachet Conjecture) Calculator?

algorithm: A process to solve a problem in a set amount of time
floor: the greatest integer that is less than or equal to x
integer: a whole number; a number that is not a fraction
...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...
lagrange theorem: in group theory, for any finite group say G, the order of subgroup H of group G divides the order of G
p = a² + b² + c² + d²
maximum: the greatest or highest amount possible or attained
minimum: the least or lowest amount possible or attained
natural number: the positive integers (whole numbers)
1, 2, 3, ...