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p | (x^2_0 - x_0 + 3)

Source: China TST 1992, problem 3

June 27, 2005
quadraticsmodular arithmeticnumber theory unsolvednumber theory

Problem Statement

For any prime pp, prove that there exists integer x0x_0 such that p∣(x02−x0+3)p | (x^2_0 - x_0 + 3) ⇔\Leftrightarrow there exists integer y0y_0 such that p∣(y02−y0+25).p | (y^2_0 - y_0 + 25).
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