Number Theory
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What is the smallest possible integer that is neither a prime or a square, and has no prime factor less than 50? *
15 points
What is the largest integer n, for which 5^n is a factor of the sum 98!+99!+100! *
20 points
Find the unit digit of 13^2020 *
15 points
Find the tens digit of 7^2019 *
15 points
Lou has a number of 3^2017. He adds up the sum of all the digits, and goes on and on. What will be the one-digit number at the end? *
15 points
Mrs. Sanders has three grandchildren, who call her regularly. One calls her every three days, one calls her every four days, and one calls her every five days. All three called her on December 31, 2016. On how many days during the next year did she not receive a phone call from any of her grandchildren? *
20 points
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