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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
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Probability of satisfying the congruent mod equation
I'm wondering about the probability of picking three different numbers $x,y,z$ out of the set $[50]=\left\{ 1,2,3,...,50\right\}$ satisfying the equation: $$xyz\equiv \gcd(x,y,z)\mod 7$$ I started out …