Number Theory

Modular Arithmetic Operations

Modular Arithmetic - Multiplication

         

Given that 2201(mod3)and5101(mod3), 2^{20} \equiv 1 \pmod{3} \quad \text{and} \quad 5^{10} \equiv 1 \pmod{3}, what is the remainder when 220×510 2^{20} \times 5^{10} is divided by 3?

What is 78×49(mod26) 78 \times 49 \pmod{26} ?

What is (6666)15 6’s mod7?\underbrace{\left(6\cdot 6 \cdot 6 \cdots 6\right)}_{\text{15 6's}} \ \bmod{7}?

What is equivalent to

1!+2!+3!++100!(mod12)? 1!+2!+3!+ \cdots + 100! \pmod{12}?

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

What is (10×85)(mod5)? (10 \times 85) \pmod{5} ?

×

Problem Loading...

Note Loading...

Set Loading...