Category Archives: Number Theory

________ What is the sum of all integer values of $n$ such that $\dfrac{20}{2n-1}$ is an integer? ________ What is the units digit of the sum of the sum of all the integers from 100 to 202 inclusive? ________ How … Continue reading →

________ In base $b$, $441_b$ is equal to $n^2$ in base 10, and $351_b$ is equal to $(n-2)^2$. What is the value of $b$, expressed in base 10? ________ The base-three representation of $0.\overline{12}$ is equivalent to what base-ten common … Continue reading →

________ Some positive integers have exactly four positive factors. For example, 35 has only 1, 5, 7, and 35 as its factors. What is the sum of the smallest five positive integers that have exactly four factors. ________ What is … Continue reading →