Number Theory
# Modular Arithmetic Operations

What is $78 \times 49 \pmod{26}$?

What is $\underbrace{\left(6\cdot 6 \cdot 6 \cdots 6\right)}_{\text{15 6's}} \ \bmod{7}?$

What is equivalent to

$1!+2!+3!+ \cdots + 100! \pmod{12}?$

Give your answer as an integer between 0 and 11, inclusive.

What is $(10 \times 85) \pmod{5} ?$