Back to all chapters
# Modular Arithmetic Operations

Considering the remainder "modulo" an integer is a powerful, foundational tool in Number Theory. You already use in clocks and work modulo 12.

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 \( 2 ^ {7} \pmod{10} ?\)

×

Problem Loading...

Note Loading...

Set Loading...