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Results tagged with nt.number-theory
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user 126667
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
12
votes
2
answers
1k
views
$Ax^2 + By^3$ representing infinitely many primes
Are there any known results of the form
there are infinitely many primes of the form $Ax^2 + By^3$
for integers $A$, $B$?
Assuming there are currently no known results of this form, what is the …
- 25.2k
20
votes
Intuition behind counterexample of Euler's sum of powers conjecture
Even simply generating all quadruples $(a, b, c, d)$ with $1 \le a \le b \le c \le d \le 133$ should work fine. There are only about 13 million such quadruples. For each, we need to add together the f …
- 25.2k
12
votes
Accepted
Why the search for ever larger primes?
Well the M in GIMPS stands for Mersenne, and it hasn't been proven that there are infinitely many Mersenne primes. But it's widely believed to be true--in fact there is a conjectural estimate of thei …
- 25.2k