In number theory, Meyer's theorem on quadratic forms states that an indefinite quadratic form Q in five or more variables over the field of rational numbers nontrivially represents zero.
By clearing the denominators, an integral solution x may also be found.
Meyer's theorem is usually deduced from the Hasse–Minkowski theorem (which was proved later) and the following statement: Meyer's theorem is the best possible with respect to the number of variables: there are indefinite rational quadratic forms Q in four variables which do not represent zero.
One family of examples is given by where p is a prime number that is congruent to 3 modulo 4.
This can be proved by the method of infinite descent using the fact that, if the sum of two perfect squares is divisible by such a p, then each summand is divisible by p.