MathDB
Show that there exists natural m - Euler's Function

Source: IMO LongList 1982 - P9

March 16, 2011
functionfloor functionnumber theory proposednumber theory

Problem Statement

Given any two real numbers α\alpha and β,0≤α<β≤1\beta , 0 \leq \alpha < \beta \leq 1, prove that there exists a natural number mm such that α<ϕ(m)m<β.\alpha < \frac{\phi(m)}{m} < \beta.
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