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. In other words, if the equation Q(x) = 0 has a non-zero real solution, then it has a non-zero rational solution. 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: ℚp of p-adic numbers for all p. 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 Q(x1,x2,x3,x4) = x2 1 + x2 2 − px2 3 − px2 4 , 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.