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On the $\mathsf{LCM}$ of a set of integers defined by moduli of powers

For integers $a,b,t$ define $$\mathcal R_t(a,b)=\{q\in\mathbb Z\cap[1,\min(a^t,b^t)]: a^t\equiv b^t\bmod q\}$$ and $\mathsf{LCM}(\mathcal R_t(a,b))$ to be $\mathsf{LCM}$ of all entries in $\mathcal ...
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