We know how to define $\frac a{a'}\bmod\frac b{b'}$ when $b'=1$, $(a',b)=1$ and $(a,{a'},b)\in\Bbb Z\times\Bbb Z\times\Bbb Z_{\neq0}$ holds.
Is there a consistent definition when $b'\in\Bbb Z\backslash\{0,1\}$ holds?
On defining a modular arithmetic.
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number-theory
elementary-number-theory
modular-arithmetic
inverse
euclidean-algorithm
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1I don't think so. – 2017-01-15
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0Is it interesting in any way? – 2017-01-15