The following proposition (which I consider true) allows to substitute (1) the congruence relation in modular arithmetic modulo all prime numbers with (2) the equality relation in integer arithmetic: \begin{equation} \forall A, B \in \mathbb{Z} : ( \; A = B \; \Leftrightarrow \; \forall p \in \mathbb{P} : A \equiv B \pmod{p} \; ) \end{equation} Does this proposition have a name?
2026-03-31 23:49:18.1775000958
Name of the theorem for substituting integer arithmetic with modular arithmetic modulo all primes
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