Find the smallest positive integer such that the congruency above fails to hold.
What is the remainder when
is divided by 2016?
A degree monic polynomial has (not necessarily distinct) integer roots. Given that , how many ordered quintuplets of roots satisfy the property that has the same units digit as
Let denote Euler's Totient Function. If the greatest common divisor of the positive integers and is 7, and find the least possible value of .
Suppose it takes digits in the binary expansion of for it to repeat. What is the minimum value of ?
As an example, in base two, which takes two digits to repeat.