$(a,b)$ is a couple of twin primes such that $b=a+2$ and $a > 29$.
Let $N = 4^b$ and $q$ the quotient which results from the division of $N$ by $a$ and $r$ is the remainder.
We calculate $P = (q\bmod b)a+r-1$
Below we prove that $P = 3(10b+1)$ using Fermat's little theorem.
$N=16\cdot4^a\equiv64...
Let $S = \{ x^2 : x \in \Bbb{Z}\}$. It forms a mult. submonoid of $\Bbb{Z}$. Define $\Omega: \Bbb{Q}^{\times} \to \Bbb{Z}$ to be $\Omega(\dfrac{a}{b}) = \Omega(a) - \Omega(b)$. It forms a group homomorphism. So it's kernel $K = \ker \Omega$ is the set of all fractions $\dfrac{q_1\cdots q_n}{r...
I had dupe-hammered this question, but it was inadvertently reopened by another gold-badge holder. I suggest to close the question again, the given answer does not add anything to the solutions given before.
Let $S = \{ x^2 : x \in \Bbb{Z}\}$. It forms a mult. submonoid of $\Bbb{Z}$. Define $\Omega: \Bbb{Q}^{\times} \to \Bbb{Z}$ to be $\Omega(\dfrac{a}{b}) = \Omega(a) - \Omega(b)$. It forms a group homomorphism. So it's kernel $K = \ker \Omega$ is the set of all fractions $\dfrac{q_1\cdots q_n}{r...
