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Results tagged with nt.number-theory
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user 117220
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
8
votes
Accepted
What is so special about $a^3+b^3+c^3 = (13m)^3$?
A solution of (1) must contain $0, 2$ or $4$ terms divisible by $13$. Essentially, this is because the only cubic residues mod $13$ are $0, 1, 5, 8, 12$, and there is no combination (with or without …
- 216
2
votes
Solutions in primes of the equation $\,3p^2+q^2=r^2+3$
Generalizing in another way from the solution $(3,5,7)$, there is also a class of solutions in which $(q,r)$ is a pair of twin primes ($q<r$). A parametric solution with $r=q+2$ is:
$$(p,q,r)=(2m+1, …
- 216