- #1

lukem

- 3

- 0

I am trying to simplify a set of equations to something easier to work with. For example

11x+4

13x+11

31x+17

19x+2

14x+9

Over integer values for x, I need to find numbers that won't be hit by these equations. The first one hits 4,15,26,37,48,59 for x=0,1,2,3,4,5. Is there a way to find a number that won't be in any set, for any range of x values? I know for a single equation, 11x+5 wouldn't ever be the same as 11x + 4, but is there a way to find an equation that won't be in any of the sets, or even a reliable way to find one number that won't be in those sets (without comparing results manually). I don't care about lines crossing on a graph of these if they were y(x) functions, I just need to know which integers don't get picked by anyone of the expressions for integer values of x. I'm trying to combine 50 of these "rules" and find numbers that never get hit.

Sorry about the wording, I really have no idea how to present this question.

Thanks!