I was reading Elementary Number Theory Second Edition by Dudley Underwood, and I came across what appeared to me to be a contradiction in chapter/section 5.
The book says: If one integer satisfies $ax \equiv b $ (mod m) $\implies $ there are infinitley many
Then the book says: if gcd$(a,m) = 1$, then $ax \equiv b $ (mod m) has exactly one solution.
What am I missing? Thanks
gcd$(a,m)=1$, then $ax≡b$ $\pmod m$ has exactly one solution $x$ < $m$. There are infinitely many solutions, and each one is congruent to $x \pmod m$.