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Divisibility Calculator

Enter two numbers to check if the first number is divisible by the second number: Check
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Random Math Shape

 Show random mathematical shape.

A Ring of Polynomial over a Field of Characteristic 2 Must Have This Property

  Let \( K \) be a finite field. \( 1 + 1 = 0 \) in K if and only if for any \( f \in K \left [ x \right ] \) such that the degree of \( f \) is more or equal to 1, the polynomial \( f(X^2) \) is a reducible polynomial.

Proof \( C \left [ a, b \right ] \) with the Norm \( \left | \left | \cdot \right | \right | _{\infty} \) is a Normed Space

Clearly the set of continuous function \( C \left [ a, b \right ] \) is a vector space. Now, we have to prove that the function \( \left | \left | \cdot \right | \right | _{\infty} :  C \left [ a, b \right ] \to \mathbb{R}  \) such that  \( \left | \left | f \right | \right | _{\infty} = \displaystyle \max_{a\leq x\leq b} \left| f(x) \right| \) for every function \( f \in C \left [ a, b \right ] \) is really a norm.

Random Species Generator

 Generate a random species.

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