MathDB
Product of two consecutive integers greater than 2

Source: IMO ShortList 1988, Problem 22, South Korea 2, Problem 63 of ILL

November 3, 2005
number theoryrelatively primequadraticsIMO Shortlistequation

Problem Statement

Let p p be the product of two consecutive integers greater than 2. Show that there are no integers x1,x2,…,xp x_1, x_2, \ldots, x_p satisfying the equation \sum^p_{i \equal{} 1} x^2_i \minus{} \frac {4}{4 \cdot p \plus{} 1} \left( \sum^p_{i \equal{} 1} x_i \right)^2 \equal{} 1 OR Show that there are only two values of p p for which there are integers x1,x2,…,xp x_1, x_2, \ldots, x_p satisfying \sum^p_{i \equal{} 1} x^2_i \minus{} \frac {4}{4 \cdot p \plus{} 1} \left( \sum^p_{i \equal{} 1} x_i \right)^2 \equal{} 1
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