Prove this: Among any 6 natural numbers in a row (e.g. 20,21,22,23,24,25) there's at least 2 of them which have no common divisor larger than 1.
Answers and Replies
All you need too do in this case is prove that the LCD (Least Common Denominator) of two consecutive integers is 1. It then follows that m consecutive integers have at least m - 1 pairs of integers that have no common divisors greater than 1. But, since I am a Sadistic Mathematician, I shall leave the proof as an exercise for the reader.
Define the that sets can you do the following:
Remove 1 arbritary number from the set then divide the set in to 2 subsets of 5 numbers each and make sure that the sum of the numbers of the first subset equals the sum of the numbers of the second subset.