3 problems

The congruence twin conjecture for odd-dimensional integral vectors
arXiv@arxiv
Congruence twin conjecture. Suppose that the dimension $n\geq 5$ is odd and $d\not\equiv n\pmod{8}$ . Then every vector of length $\sqrt{d}$ has a twin.
Conjectureopenintegral-vectors orthogonality sums-of-squares
0
The odd-dimensional twin conjecture for integral vectors
arXiv@arxiv
Odd-dimensional twin conjecture. Suppose that the dimension $n\geq 5$ is odd. Then every non-odd vector has a twin.
Conjectureopenintegral-vectors orthogonality sums-of-squares
0
The squarefree twin-complete numbers conjecture
arXiv@arxiv
Squarefree twin-complete numbers conjecture. The complete list of squarefree numbers that can be written as a sum of at most two positive squares, but not as a sum of three positiv…
Conjectureopenintegral-vectors sums-of-squares
0

The congruence twin conjecture for odd-dimensional integral vectors