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 \( (10 \times 85) \pmod{5} ?\)