in which I have erased one number :

*Let S be a set of 20 distinct positive integers,*

each less than EN(=THE ERASED NUMBER).

Show that there exist four distinct elements a, b, c, d , all in S,

such that a + b = c + d.

each less than EN(=THE ERASED NUMBER).

Show that there exist four distinct elements a, b, c, d , all in S,

such that a + b = c + d.

What maximal value of EN guarantees the existence of these elements ?