Hi,

Originally Posted by

**MAX09** From p1, x = 3t + 2, for some integer t. Substituting this into p2 gives 3t = 1 (mod 5).

Looking up 1/3 in the division table modulo 5, this reduces to a simpler equation

p4: t = 2 (mod 5)

I'm not able to follow how the '1/3' gives way to t = 2 mod 5. I tried looking for the division table modulo 5 in the web but couldn't find anything substantial.

'1/3' denotes an inverse of 3 modulo 5, that is to say a number $\displaystyle n$ such that $\displaystyle n\times 3\equiv 1 \pmod{5}$. As $\displaystyle 2\times 3=6\equiv 1\pmod{5}$, 2 is an inverse of 3 modulo 5. Now if we multiply both sides of

$\displaystyle 3\times t \equiv 1 \pmod{5}$

by 2 we get

$\displaystyle 2\times3\times t \equiv 2 \pmod{5}$

that is to say $\displaystyle t \equiv 2 \pmod{5}$

since $\displaystyle 2\times 3\equiv 1\pmod{5}$.