- Markoff Surfaces and Strong Approximation
- Project Year:
2022
- REU Student (s):
Enver Aman | Rutgers University-New Brunswick NJ
- Student 1 Institution:
Rutgers University-New Brunswick
- Project Mentor:
Alex Kontorovich
- Project Mentor Area:
Mathematics
- Project Abstract:
The Markoff equation is the equation x2 + y2 + z2 = 3xyz: we are interested in the solutions of this equation over Z or Fp, for a prime p. The Strong Approximation Conjecture states that, for each prime p and nonzero solution (x1; x2; x3) to the Markoff equation modulo p, there is a corresponding solution (x1'; x2'; x3') to the same equation over Z such that xj=xj' (mod p). We worked on the properties of these solutions.
