I am asked:
Prove that if n+1 distinct numbers are selected from the first 2n positive integers {1,2,3,...,2n-1,2n} then at least two of the n+1 numbers are co-prime where n is a positive integer
I know 32 divides evenly into 64 and 96, but 32 is bigger than 16 and 20 so could not even divide. However 3+2=5 which can't get smaller.
How can I prove this?