If, for natural numbers 𝑎,𝑏,𝑛

\[a \times b \equiv 1 \pmod n\]

is it obvious that either
\[a \equiv b \equiv 1 \pmod n\]
or
\[a \equiv b \equiv -1 \pmod n\]

Does this require special justification?

(is it one of those maths results that looks obvious but isn't)

#maths #numbertheory