MathDB

56

Part of 1969 IMO Shortlist

Problems(1)

Inequaity on natural numbers and nth root.

Source:

10/4/2010
Let aa and bb be two natural numbers that have an equal number nn of digits in their decimal expansions. The first mm digits (from left to right) of the numbers aa and bb are equal. Prove that if m>n2,m >\frac{n}{2}, then a1n−b1n<1na^{\frac{1}{n}} -b^{\frac{1}{n}} <\frac{1}{n}
decimal representationInequalitycalculusIMO ShortlistIMO Longlist