Quandaries
and Queries 

Who is asking: Student Level: Middle Question: Note: x means multiplied by. 

Hi, What a neat problem! But why is it that they have to mess it up by bringing in Amy and Boris. Why not just say "find all possible common divisors of 2n+1 and 3n+9"? Clearly 1 divides them both, but that's not very exciting. The key is to first look for primes that divide 2n+1 and 3n+9. If the prime p were a common divisor, then 2n+1 = kp, which makes 3n+9 equal to 3(kp + 5)/2. What primes divide 3(kp + 5)? 3 divides 3(kp + 5). What other prime might divide 3(kp + 5)? Chris and Penny 

