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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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density of primes of the form $8k+1$ with the given condition

Let $P$ be the set of all primes of the form $8k+1$. Can we say anything about the density of primes $p$ in this set such that if $x^2=2$ in $\mathbb F_p$, then $x+1$ is a square in $\mathbb F_p$? (No …
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