# inversing using Euclid's algorithm [closed]

The question is:

Find the inverse of 14 mod 37. I don't know how to do, so could someone please explain it? Thanks in advance.

• Do you mean multiplicative inverse? That is you want to find an element $x$ such that $14x\equiv 1\pmod{37}$? – Peter Woolfitt Jan 29 '15 at 20:58

Hint $\$ Using what I call Gauss's algorithm (a special form of Euclid's algorithm)
${\rm mod}\ 37\!:\,\ \dfrac{1}{14}\,\equiv\,\dfrac{2}{28}\,\equiv\,\dfrac{2}{-9\ }\,\equiv\,\dfrac{8}{-36\ }\equiv\, \dfrac{8}1$