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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
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
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
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