对整数a >= 2与n >= 1,a^n + 1是素数,证明
如果对某个整数
与
,
是素数,证明n一定是2的幂。
证明:
Let
which is not power of 2, and
.
Obviously n is an odd number.
Then we have
.
Therefore,
hava a divisor which is
. And this can show that
is a composite number.
So n must be the power of 2.
Obviously n is an odd number.
Then we have
Therefore,
So n must be the power of 2.