Lagrange number [SEP] named after
, but this time the number is the problem. If we don't allow then we can increase the number on the right hand side of the inequality from 2 to /5. Repeating this process we get an infinite sequence of numbers , 2, /5, ... which converge to 3. These numbers are called the Lagrange numbers, and are named after Joseph Louis Lagrange.
Relation to Markov numbers.
The "n"th Lagrange number "L" is given by
where "m" is the "n"th Markov number
Lagrange's theorem (number theory)
In number theory, Lagrange's theorem is a statement named after Joseph-Louis Lagrange about how frequently a polynomial over the integers may evaluate to a multiple of a fixed prime. More precisely, it states that if "p" is a prime number and formula_1 is a polynomial with integer coefficients, then either:
- every coefficient of "f"("x") is divisible by "p", or
- has at most incongruent solutions.
Solutions are "incongruent" if