Suppose we have integers $a$,$\space b$ and $m$ with $m \gt 1$. Prove that if the product $a*b$ has a multiplicative inverse modulo m, then so does each of $a$ and $b$.
Prove that if the product of $a$ and $b$ has multiplicative inverse modulo $m$
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number-theory
elementary-number-theory
1 Answers
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$1\pmod m=(ab)x=a(bx)=(ax)b$