I want to calculate the value of $a$, given the equation:
$-8a\equiv 12 \mod26$
I know that i have to find the multiplicative inverse of $-8$, but since $\gcd(-8,26) \neq 1$, I suspect there can be 0 or many multiplicative inverses. Is this true ?
I read the wiki page, but it only says that if $\gcd(-8,26) = 1$ then I have a unique modular inverse, but it doesn't explain what happens in the general case…
Best Answer
Note that$$-8a\equiv12\pmod{26}\iff-4a\equiv6\pmod{13}.$$Can you take it from here?