Reply To: Maths
@frazza238, #98502
Well done for getting this far! Some comments:
- You are correct that the only solution in (a,b,p) is (1,1,2). Congratulations!
- You are also correct that p divides a+b – or, if you like, that a+b=0 modulo p. (I assume this is what you mean by 0=-a-b.) However…
- …the point above does not necessarily imply a=b=0. (e.g. (a,b,p)=(2,4,3) satisfies said conditions.) For this bit you can definitely assume p>2 (you did the p=2 case!), and see if you can put some bounds on a and b. [Hint: Why must a<p? And can you strengthen this?]
Good luck!