- #1
razmtaz
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Homework Statement
if an integer n >= 2 and if n divides ((n-1)! +1) prove that n is prime.
Homework Equations
a divides b iff b = ma for integers a, b, m.
The Attempt at a Solution
by contrapositive:
Assume n is not prime. Then we have by definition of divisibility
((n-1)*(n-2)*...*2) + 1 = n*a for integer a
but since n is greater than all of the individual factors of (n-1)!, then clearly it shares no factors with the LHS above, so we have a contradiction. thus, n is prime.
This seems correct to me, but I am unsure about the part where I say clearly it shares no factors with the LHS. I would think that it doesnt, but am not 100% sure. Can somebody tell me where my reasoning went wrong and how i should go about fixing it? or perhaps tell me a better proof method to attack the problem with? or tell me i am correct? : )