MathCounts Training – Number Theory – 3

Posted on September 1, 2023 by kevin
  1. ________ What is the sum of all integer values of $n$ such that $\dfrac{20}{2n-1}$ is an integer?
  2. ________ What is the units digit of the sum of the sum of all the integers from 100 to 202 inclusive?
  3. ________ How many of the divisors of $8!$ are larger than $7!$?
  4. ________ If $n$ is a prime number, what is the smallest composite number produced by $n^2-n-1$?
  5. ________ $A$, $B$, $C$, and $D$ are distinct positive integers such that the product $AB=60$, the product $CD=60$ and $A-B=C+D$. What is the value of $A$?
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