Number Theory
# Modular Arithmetic Operations

Find the last digit when

\[\color{blue}1^{\color{blue}1} + \color{green}2^{\color{green}2} + \color{purple}3^{ \color{purple}3} + \cdots + \color{red}9^{ \color{red}9} + \color{violet}{10}^{\color{violet}{10}} \]

is written out as an integer.

What is \( 5 ^ {-1} \pmod{17} ?\)

**Hint:** Remember that inverses multiply to 1.

What is the sum of all possible primes \(p\) such that \(p^2+8\) is also a prime?

How many natural numbers \(n\) exist such that the following are all primes?

\[3n-4 \qquad 4n-5 \qquad 5n-3\]

×

Problem Loading...

Note Loading...

Set Loading...