The positive integers $N$ and $N^2$ both end in the same sequence of four digits $abcd$ when written in base 10, where digit $a$ is not zero. Find the three-digit number $abc$.

What is the last digit of $9^{2019}$?

What are the last two digits of $8^{88}$?

Find the remainder when $3^{2019} + 4^{2019}$ is divided by 5?

Find the remainder when $9 \times 99 \times 999 \times \cdots \times \underbrace{99\cdots9}_{\text{999}}$ is divided by $1000$.

What is the units digit of the sum of the squares of the integers from $1$ to $2015$, inclusive?

What are the last two digits in the sum of the factorials of the first $100$ positive integers?

What is the tens digit of $7^{2019}$?

What is the units digit of $13^{2019}$?

What are the sign and units digit of the product of all the odd negative integers strictly greater than $-2015$?

What is the hundreds digit of $2011^{2011}?$

The number obtained from the last two non-zero digits of $90!$ is equal to $n$. What is $n$?

Let $k={2008}^{2}+{2}^{2008}$. What is the units digit of $k^2+2^k$?

What is the tens digit in the sum $7!+8!+9!+...+2018!$

What is the units digit of the product $7^{23} \times 8^{105} \times 3^{18}$?

When $(37 \times 45) - 15$ is simplified, what is the units digit?

Find the smallest positive integer $n$ such that the last $3$ digits of $n^3$ is $888$.

Find all positive integer $n$ such that $n$ is a square and its last four digits are the same.

What is the last digit of $17^{17^{17^{17}}}$?

If for any integer $k\ne 27$ and $\big(a-k^{2015}\big)$ is divisible by $(27-k)$, what is the last two digits of $a$?

Determine the units digit of the sum $0!+1!+2!+\cdots+n!+\cdots+20!$?

What is the units digit of $-1\times 2008 + 2 \times 2007 - 3\times 2006 + 4\times 2005 +\cdots-1003\times 1006 + 1004 \times 1005$?

What is the last digit of $7^{222}$?

What is the tens digit of $2015^{2016}-2017?$

What is the tens digit of $321^{123}$?