Question

Известно, что a=3^2009+2.Верно ли, что a^2+2-простое число? Обоснуйте.

Answer 1

Если обозначить n=2009, а=3^n+2, тогда
а^2+2=(3^n+2)^2+2=3^(2n)+4*3^n+4+2=3^(2n)+4*3^n+6=
=3(3^(2n-1)+2*3^(n-1)+2). Т.е., число делится на 3, значит составное.

Answer 2

Checking if a^2 + 2 is a Prime Number

The value of a is given as a = 3^2009 + 2. We need to determine if a^2 + 2 is a prime number.

To do this, we can calculate the value of a^2 + 2 and then analyze its primality.

First, let's calculate the value of a^2 + 2: a^2 + 2 = (3^2009 + 2)^2 + 2

Calculating this value will help us determine if a^2 + 2 is a prime number.

Let's proceed with the calculation: a^2 + 2 = (3^2009 + 2)^2 + 2

a = 3**2009 + 2
result = a**2 + 2
result

The result of the calculation will help us determine if a^2 + 2 is a prime number.

After calculating the value of a^2 + 2, we can analyze its primality to determine if it is a prime number.