  Mohammed Ben Alhocain, in an Arab manuscript of the tenth century, stated
that the principal object of the theory of rational right triangles is to find
a square which when increased or diminished by a certain number $m$ becomes a
square (see Dickson). In modern language, this object is to find a rational
point of infinite order on the elliptic curve $my^2=x^3-x$. Heegner constructed
(see also Monsky) such rational points in the case that $m$ are primes
congruent to 5, 7 modulo 8 or twice primes congruent to 6 modulo 8. We extend
Heegner's result to integers $m$ with many prime divisors.
