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

1 vote
1 answer
123 views

Simultaneous rational approximations of multiples of the golden ratio

My question concerns potential simultaneous rational approximations of irrational numbers. Let $\alpha = \frac{1 + \sqrt{5}}{2}$ be the golden ratio, and $k \in \mathbb{N}$ a positive integer. In what …
1 vote
2 answers
649 views

Asymptotic of the sum of squared primes [closed]

I have a rather simple question of number theory which I can't seem to be able to find a good reference for. I am not a specialist and I don't really know where to look. I would like to show that the …