MathDB

22

Part of 1988 IMO Shortlist

Problems(1)

Product of two consecutive integers greater than 2

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

11/3/2005
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
number theoryrelatively primequadraticsIMO Shortlistequation