5 problems

Pollock's conjecture. Every positive integer is the sum of at most five tetrahedral numbers, seven octahedral numbers, nine cubes, thirteen icosahedral numbers, and twenty-one dode…

Let $S_n$ denote the $n$-th square pyramidal number, defined by … The Cannonball Problem asks which numbers are both square and square pyramidal. Lucas's cannonball conjecture. The…

Let $n$ and $p$ be positive integers. For a permutation $\sigma$ of $\{1,2,\ldots,p\}$, consider the $p$-dimensional simplex … formed by cutting the $p$-dimensional cube…

Platonic-number sum conjecture. Every integer can be written as a sum of at most five different platonic numbers.

Conjecture on tetrahedral numbers. Every number is the sum of at most five tetrahedral numbers. This is presented as another open problem concerning representations of integers by…