Algebra · Completing the square · Quadratic inequalities · Lattice points
Find all pairs of integers \(p\) and \(q\) for which the inequalities
\[ p^{2} + q^{2} < 18p - 20q - 166, \qquad 32p - q^{2} > p^{2} + 12q + 271 \]
hold simultaneously.
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Serbian Municipal Competition 1996, high school grade I, problem 2. Organized by the Mathematical Society of Serbia (DMS).