Qn about CS1231S
How to prove that if 2^n+1 is a prime, then n is a power of 2?
Qn about CS1231S
That statement is false
Counter example:
2^32+1=4294967297=6700417*641
2^32+1=4294967297=6700417*641
That statement is falseCounter example:
2^32+1=4294967297=6700417*641
you are wrong
pls look at the question again. saying if 2^p+1 is a prime, then p is the power of 2. You just showed that the reverse statement is wrong. The original statement is correct.
come in
if n is not a power of 2, then there exists an odd prime dividing n, say p. then, n=pq.
then,
2^n+1=2^pq+1=(2^q+1)(2^(p-1)q-2^(p-2)q+...+2^2q-2^q+1)
and p is odd, LHS=RHS.
QED.
then,
2^n+1=2^pq+1=(2^q+1)(2^(p-1)q-2^(p-2)q+...+2^2q-2^q+1)
and p is odd, LHS=RHS.
QED.
you are wrongpls look at the question again. saying if 2^p+1 is a prime, then p is the power of 2. You just showed that the reverse statement is wrong. The original statement is correct.
you are right : )
come inif n is not a power of 2, then there exists an odd prime dividing n, say p. then, n=pq.
then,
2^n+1=2^pq+1=(2^q+1)(2^(p-1)q-2^(p-2)q+...+2^2q-2^q+1)
and p is odd, LHS=RHS.
QED.
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