prove by contradiction that 3 is the only prime number which is 1 less than a square number
Question
Solution 1
Sure, here is the proof by contradiction:
Assume that there is a prime number p that is 1 less than a square number, and p is not equal to 3.
This means that p can be written as n^2 - 1 for some integer n.
We can factor the expression n^2 - 1 into (n-1)(n+1).
So, p = (n-1)(n+1).
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