Tagged Questions

Questions on more advanced topics of number theory, such as quadratic residues, primitive roots, prime numbers, non-linear Diophantine equations, etc. Consider first if (elementary-number-theory) might be a more appropriate tag before adding this tag.

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$2^i - 2293$ is always composite?

Is $2^i - 2293$ always composite for i=1,2,3,...? I have known: if $2^i - 2293$ is prime, i must have the form $i = 24 k+1$ ...
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Finding order of a point on eliptic curve

Just started studying eliptic curves and am having trouble with this question. An explanation/solution would be much appreciated. Find the order of the point X on the elliptic curve $E/Q$ for the ...
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Is $\prod_{n=1}^\infty P_{2n-1}$ regularizable?

Assume that $P_n$ denotes the $n$'th prime for this entire question. Inspriation: I was dumbfounded by the fact that: $$\hat\prod_\limits{n=1}^\infty P_{n}=4\pi^2$$ After further investigation, I ...
Let p=3 (mod 4) be a prime, and $E/F_{p^r}$ be the elliptic curve given by $y^2 = x^3 − x$ Find the zeta-function of $E/F_p$ and use it to determine $|E(F_{p^r} )|$ for all r>0.