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A Diophantine equation is an equation that only takes integer coefficients, and that can be written as f(x_1, x_2, x_3, . . ., x_n) = 0, where f is a polynomial. Diophantine analysis is a branch of mathematical analysis, concerned with such equations. Typical questions include:

  1. Are there any solutions?
  2. Are there any solutions beyond some that are easily found by inspection?
  3. Are there finitely or infinitely many solutions?
  4. Can all solutions be found in theory?
  5. Can one in practice compute a full list of solutions?
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