MathDB
Rational Square Root

Source: OME 2014 2

July 16, 2014
number theory unsolvednumber theory

Problem Statement

Given the rational numbers rr, qq, and nn, such that 1r+qn+1q+rn=1r+q\displaystyle\frac1{r+qn}+\frac1{q+rn}=\frac1{r+q}, prove that n−3n+1\displaystyle\sqrt{\frac{n-3}{n+1}} is a rational number.
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