Excel in math and science

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Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable. Find out if you're right!

That seems reasonable. Find out if you're right!

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Number Theory

Euler's Theorem

Intro

Concept Quizzes

Warmup
Fermat's Little Theorem
Euler's Totient Function
Euler's Theorem
Last Digits
Diffie-Hellman
RSA

Challenge Quizzes

Level 2
Level 3
Level 4
Level 5

Euler's Totient Function

Given that $30=2\times3\times5$ , what is the value of the Euler totient function of 30, i.e. what is $\phi(30)$ ?

6 8 10 12

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by Brilliant Staff

Given that the only prime factors of a certain positive integer $n$ are 2 and 3, find (in terms of $n$ ) the number of positive integers less than or equal to $n$ that are coprime to $n$ .

\frac n2

\frac n3

\frac n6

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by Brilliant Staff

$\dfrac1{24} , \dfrac{2}{24}, \dfrac{3}{24}, \ldots , \dfrac{23}{24}, \dfrac{24}{24}$

How many of the fractions above cannot be reduced?

6 8 10 12

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by Brilliant Staff

$\dfrac1{32} , \dfrac{2}{32}, \dfrac{3}{32}, \ldots , \dfrac{31}{32}, \dfrac{32}{32}$

Which of the following is true regarding the 32 fractions above?

Statement 1: The number of fractions that cannot be reduced is less than the number of fractions that can be reduced.

Statement 2: The number of fractions that cannot be reduced is equal to the number of fractions that can be reduced.

Statement 3: The number of fractions that cannot be reduced is greater than the number of fractions that can be reduced.

Statement 1 Statement 2 Statement 3

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by Brilliant Staff

Let $A$ denote the number of positive integers less than or equal to 11 that are coprime with 11.

Let $B$ denote the number of positive integers less than or equal to 12 that are coprime with 12.

Which one is larger, $A$ or $B$ ?

A

is larger than

B

B

is larger than

A

They are equal

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by Brilliant Staff

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Euler's Theorem

Intro

Concept Quizzes

Challenge Quizzes

Euler's Totient Function

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.