×

## Basic Applications of Modular Arithmetic

Solve integer equations, determine remainders of powers, and much more with the power of Modular Arithmetic.

# Level 3

Find the remainder when $$3^{247}$$ is divided by $$17$$.

$\Large 1+\dfrac{1}{2} + \dfrac{1}{3} + \ldots + \dfrac{1}{23} = \dfrac{a}{23!}$

Find the remainder when $$a$$ is divided by 13.

###### Try this set RMO Practice Problems

Find the last three digits of the number $3 \times 7 \times 11 \times 15 \times \ldots \times 2003$

Find the smallest positive integer $$N$$ such that $$13^N \equiv 1 \pmod{2013}$$.

Details and assumptions

• You may choose to refer to Modulo Arithmetic notation.

• 0 is not a positive integer.

Find the GCD of $$(19! + 19, 20! + 19).$$

Details and Assumptions:

• Here GCD denotes greatest common divisor.
×