Waste less time on Facebook — follow Brilliant.
Already have an account? Log in here.
Basic Applications of Modular Arithmetic
Solve integer equations, determine remainders of powers, and much more with the power of Modular Arithmetic.
Find the remainder when \(3^{247}\) is divided by \(17\).
Already have an account? Log in here.
by
Mardokay Mosazghi
\[\Large 1+\dfrac{1}{2} + \dfrac{1}{3} + \ldots + \dfrac{1}{23} = \dfrac{a}{23!}\]
Find the remainder when \(a\) is divided by 13.
Try this set RMO Practice Problems
Already have an account? Log in here.
by
Surya Prakash
Already have an account? Log in here.
by
Varun Vijay
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.
Already have an account? Log in here.
by
Calvin Lin
Find the GCD of \((19! + 19, 20! + 19).\)
Details and Assumptions:
- Here GCD denotes greatest common divisor.
Already have an account? Log in here.
by
Anuj Shikarkhane