3 problems

Conjecture on two polygonal summands. For $s\in\{4,5,6,7,8,10\}$, all natural numbers can be written as a sum of a practical number and two $s$-gonal numbers.

Conjecture on practical and polygonal sums. If $s>3$, $s \not\equiv 0\pmod{12}$, and $s \not\equiv 4\pmod{12}$, then all sufficiently large natural numbers can be written as a sum…

Let $a,b,c$ be positive integers with $2 mid ab$ and $2 divides c$. A practical number is a positive integer each of whose integers from $1$ through it can be written as a sum…