◀ ▲ ▶Branches / Number-theory / Corollary: Diophantine Equations of Congruences Have a Finite Number Of Solutions
Corollary: Diophantine Equations of Congruences Have a Finite Number Of Solutions
(related to Proposition: Diophantine Equations of Congruences)
Let m > 1 be a positive integer and let (f(x_1,\ldots,x_r))(m)=0(m) be a Diophantine equation of congruences modulo m. Then the number of distinct solutions, i.e. ordered tuples (a_1(m),\ldots,a_r(m)) solving this equation
f(a_1(m),\ldots,a_r(m))\equiv0(m)
is finite.
Example
The equation x^2(8)-1(8)\equiv 0(8) (can also be written as x^2\equiv 1\mod 8) has only the four solutions 1(8),3(8),5(8),7(8).
Table of Contents
Proofs: 1
Mentioned in:
Propositions: 1
Thank you to the contributors under CC BY-SA 4.0!

- Github:
-

References
Bibliography
- Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927
- Jones G., Jones M.: "Elementary Number Theory (Undergraduate Series)", Springer, 1998