IF pis pume number and pe
be
divides then bdivides
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We suppose the situation that p divides a and a+1 both Thus we get,
a = pr and a+1 = ps
Now you can just subtract both the equations like this:
(a+1)-a = ps - pr
Using that we get,
1 = p(s-r)
This shows that p divides 1 (as (s-r) is an Integer), which is impossible.
This proves that our assumption is wrong and p can only divide a and not a+1.
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