Abstract
We use new bounds of double exponential sums with ratios of integers from prescribed intervals to get an asymptotic formula for the number of solutions to congruences \[ ∑ j = 1 n a j x j y j ≡ a 0 ( mod p ) , \sum _{j=1}^n a_j \frac {x_j}{y_j} \equiv a_0 \pmod p, \] with variables from rather general sets.
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