Question 42
Consider the set $A = \{1, 2, 3, \dots, 100\}$.
a) Give an example of a set $B$ having 11 elements from $A$, having the property: *from any two elements from $B$, the greatest common divisor of them is at least 9*.
b) Prove that, for any subset $C$ of $A$ having 11 elements, there are two distinct elements of $C$ such that their GCD is not greater than 9.
a) Give an example of a set $B$ having 11 elements from $A$, having the property: *from any two elements from $B$, the greatest common divisor of them is at least 9*.
b) Prove that, for any subset $C$ of $A$ having 11 elements, there are two distinct elements of $C$ such that their GCD is not greater than 9.