The Vietnamese Mathematical Olympiad (VMO) is legendary in the competitive math world for its grueling multi-day format and its penchant for "beautifully difficult" geometry and functional equations.

Deep dives into roots and coefficients that require more than just Vieta’s formulas.

xn+1=xn+1⌊xn⌋x sub n plus 1 end-sub equals x sub n plus the fraction with numerator 1 and denominator the floor of x sub n end-floor end-fraction

At first glance, the sequence grows very slowly because we are adding small fractions. However, as stays within a range , we are repeatedly adding

. The beauty of the problem lies in proving that it doesn't "skip" over an integer due to the discrete steps. Why this matters Vietnamese problems frequently focus on: