Question 6
Choose 1008 distinct integers between 1 and 2014 inclusive.
a. Prove that three of them $a,b,c$ can be found such that $\gcd(a,b)$ divides $c$ (the greatest common divisor is the largest natural number dividing both integers).
b. Prove that three of them $a,b,c$ can be found such that $\gcd(a,b)$ does not divide $c$.
a. Prove that three of them $a,b,c$ can be found such that $\gcd(a,b)$ divides $c$ (the greatest common divisor is the largest natural number dividing both integers).
b. Prove that three of them $a,b,c$ can be found such that $\gcd(a,b)$ does not divide $c$.