An Integer Sign Condition

★ 8/10functions number theory Logarithms inequality Casework

Problem

Let $f(x) = ax - m$ (with $m \in \mathbb{N}^*$ ) and $g(x) = \ln\dfrac{x}{a}$ . If

f(x)\cdot g(x) \geqslant 0 \qquad \text{for every } x \in \mathbb{N}^*,

find the range of possible values of the real number $a$ .

Answer

Solution

Difficulty	8/10
Topics	functions, number theory, Logarithms, inequality, Casework

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