5 problems

Strict semi-scaledness conjecture. Every primitive Master-Hit $(a,b,m,n)$ with exactly one exponent-one blocker satisfies

Let $(a,b,m,n)\in\mathcal{M}$ be a Master-Hit, and call a prime divisor of $f_1$ that satisfies the relevant coprimality condition with $\mathcal{P}(a,b,m,n)$ a blocker. Basis-form…

Let $(a,b,m,n)\in\mathcal{M}$ be a Master-Hit, and let $f_1$ and $\mathcal{P}(a,b,m,n)$ denote the associated integer and set of primes. For a prime $\ell$, write $v_\ell(f_1)$ for…

Let $(x,y,z)$ and $(u,v,w)$ be primitive Pythagorean triples. The system … has a solution only if $(x,y,z)$ or $(u,v,w)$ equals $(1,0,1)$. The trivial-triple conjecture. If the sys…

Conjecture on combining noninteger lateral diagonals and sides. The cases when bricks have a noninteger lateral diagonal or one noninteger side may be combined into one case.