Arithmetic FrobeniusNumber Theory Level 5
I have an unlimited supply of 17-cent, 18-cent, and 19-cent stamps. I'd like to put exactly \( N \) cents' worth of postage on an envelope, but no matter which combination of stamps I try, I am unable to accomplish this.
What is the largest possible value of \( N \)?
Bonus 1: Generalize to any three consecutive integers.
Bonus 2: Generalize to any three-term arithmetic progression.
Bonus 3: Generalize to any arithmetic progression.