Given a prime number p, Lehmer raised the problem of investigating the number of integers \(\) for which a and \(\) are of opposite parity, where \(\) is such that \(\). We replace the pair \(\) by a point lying on a more general irreducible curve defined mod p and instead of the parity conditions on the coordinates more general congruence conditions are considered. An asymptotic result is then obtained for the number of such points.
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