Prove the following statement:

In any set of 26 integers chosen from the set of (1,2,3, ...50) there must be at least a pair of numbers such that one of them divides the other.

Generalize.

(In reply to

re(2): The solution is in the problem.==>not so by broll)

It is not *gilding the lily.*

Both of us agree that 26 to 50 fits the description of a largest (25 members) set where no pair of numbers has a common divisor.

Clearly, this not the only set: e.g.

replacing some of the semiprime numbers (=p*q) - with some restrictions - produces qualifying sets.

Example: Example:replace 34 by 17, 42 by 21, replace 26 or 39 (but not both!) by 13 etc.

It applies not only to semiprime numbers, pq^2 might be replaced by pq or by q^2 in some cases (50 by 25, 44 by 22 etc)...

If you want, **you may follow from here** to provide a solid proof - there not too many cases to consider.

*Edited on ***November 27, 2016, 9:19 pm**