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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.

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  • $\begingroup$ Do you mean multiplicative inverse? That is you want to find an element $x$ such that $14x\equiv 1\pmod{37}$? $\endgroup$ – Peter Woolfitt Jan 29 '15 at 20:58
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Hint $\ $ Using what I call Gauss's algorithm (a special form of Euclid's algorithm)

${\rm mod}\ 37\!:\,\ \dfrac{1}{14}\,\equiv\,\dfrac{2}{28}\,\equiv\,\dfrac{2}{-9\ }\,\equiv\,\dfrac{8}{-36\ }\equiv\, \dfrac{8}1$

Alternatively use the Extended Euclidean Algorithm in this easy format.

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