is the number <em>L</em> such that
![5L\equiv1\pmod7](https://tex.z-dn.net/?f=5L%5Cequiv1%5Cpmod7)
Consider the first 7 multiples of 5:
5, 10, 15, 20, 25, 30, 35
Taken mod 7, these are equivalent to
5, 3, 1, 6, 4, 2, 0
This tells us that 3 is the inverse of 5 mod 7, so <em>L</em> = 3.
Similarly, compute the inverses modulo 7 of 2 and 3:
![2a\equiv1\pmod7\implies a\equiv4\pmod7](https://tex.z-dn.net/?f=2a%5Cequiv1%5Cpmod7%5Cimplies%20a%5Cequiv4%5Cpmod7)
since 2*4 = 8, whose residue is 1 mod 7;
![3b\equiv1\pmod7\implies b\equiv5\pmod7](https://tex.z-dn.net/?f=3b%5Cequiv1%5Cpmod7%5Cimplies%20b%5Cequiv5%5Cpmod7)
which we got for free by finding the inverse of 5 earlier. So
![2^{-1}+3^{-1}\equiv4+5\equiv9\equiv2\pmod7](https://tex.z-dn.net/?f=2%5E%7B-1%7D%2B3%5E%7B-1%7D%5Cequiv4%2B5%5Cequiv9%5Cequiv2%5Cpmod7)
and so <em>R</em> = 2.
Then <em>L</em> - <em>R</em> = 1.