Thread: Primes

The numbers are both primes for n=1 and n=2 in which the pairs are 7, 11 and 79, 83. Prove is composite for infinitely many positive integers n and prove is composite for infinitely many n.

Note: This my first LaTex post, and I was pretty excited even though it is a simple equation.

Originally Posted by brucewayne

The numbers are both primes for n=1 and n=2 in which the pairs are 7, 11 and 79, 83. Prove is composite for infinitely many positive integers n and prove is composite for infinitely many n.

Values of n<1000 that make at least one of these two

n ={1, 2, 3, 4, 5, 7, 11, 12, 13, 18, 45, 49, 51, 55, 63, 193, 247, 260, 324, 390, 393, 610, 929,....}

Originally Posted by brucewayne

The numbers are both primes for n=1 and n=2 in which the pairs are 7, 11 and 79, 83. Prove is composite for infinitely many positive integers n and prove is composite for infinitely many n.

Note: This my first LaTex post, and I was pretty excited even though it is a simple equation.

Consider 9^n mod 7... (There might be a better mod, but this one works, anyway.)

-Dan

Modulo 7,







...and it repeats. Here, you can prove that there are infinitely many n such that , but you can't say anything about .

But if we look at it mod 11, it turns out that , , , etc. are 9 mod 11, adding 2 makes them a multiple of 11.