Hi can you please help me answer this :)
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is the number <em>L</em> such that
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:
since 2*4 = 8, whose residue is 1 mod 7;
which we got for free by finding the inverse of 5 earlier. So
and so <em>R</em> = 2.
Then <em>L</em> - <em>R</em> = 1.
We have the equation:
So then we need to distribute -7p to the parentheses:
Then we need to set the equation equal to 0, so we must subtract 21 on both sides:
Then we need to factor this. So we end up with:
This is as much as this can be factored, so <u>we cannot go any further</u>.