Number Theory
Modular Arithmetic Operations
As we've now covered modular addition and modular multiplication (repeated modular addition), the next operation to consider is repeated modular multiplication, aka modular exponentiation!
Given that \( 9 \equiv 2 \pmod{7} \), what is \[ 9 \times 9 \times 9 \times 9 \times 9 \pmod{7}? \]
What is \( 2 ^ {15} \pmod{11} ?\)
What is \( 5 ^ {34} \pmod{31} ?\)
Which of the following is congruent to \[ \large 7^{7^{7^{7^7}}} \pmod {10}? \]
What is \( 2 ^ {7} \pmod{10} ?\)