Number Theory
Basic Applications of Modular Arithmetic
Find the remainder when \(70!\) is divided by \(5183\).
Note: Don't use a computational device!
by
Krishna Ar
What is the sum of all six-digit positive integer(s) such that they satisfy the property that the number equals to the last six (rightmost) digits of its own square?
by
Pi Han Goh
\[ \large \displaystyle\sum_{k=0}^{1007!+1}{10^k}\]
Find the remainder when the summation above is divided by the summation below.
\[ \large \displaystyle\sum_{k=0}^{1008}{10^k} \]
by
Ivan Molina N
Find the largest \(n<10,000\) such that \(\displaystyle \prod_{k=0}^{n} \binom{n}{k}\) is an odd number.
by
Trevor Arashiro
\[\Huge 6^{6^{6^{6^{6^6}}}}\]
Find the \(6^\text{th}\) last digit from the right of the decimal representation of the above number.
by
Cody Johnson