The problem involves finding the maximum size of a subset, P, from the set {1, 2, 3, ..., 50} such that no pair of distinct elements in P has a sum that is divisible by 7. The discussion revolves around understanding the implications of including certain numbers in the subset and the resulting exclusions based on modular arithmetic.
The discussion is active, with participants questioning the inclusion of certain numbers and exploring the consequences of those choices. There is a focus on identifying which numbers cannot be included in the subset based on the modular conditions established.
Participants reference modular arithmetic, specifically modulo 7, to determine which numbers can coexist in the subset without violating the problem's conditions. There is an ongoing exploration of the relationships between the numbers and their residues modulo 7.
icystrike said:
icystrike said:
tiny-tim said:no, that's what could be in p … what can't be in p are 6 13 20 27 34 41 48, in other words everything = -1 (mod 7)
suppose 2 and 3 are also in p (as well as 1) … now what can't be in p?
icystrike said: