Two improved lower bounds for the 2-adic valuation of the constant of the Prouhet-Tarry-Escott problem
Source: hexagonmath.org/abs/2611.00058v1
For an ideal solution of the Prouhet--Tarry--Escott problem of size $n$ the associated constant $C$ is divisible by a large power of $2$. Restricting to symmetric solutions, we prove two new lower bounds for $v_2(C)$: $v_2(C)\ge14$ at $n=15$, improving $12$, and $v_2(C)\ge19$ at $n=20$, improving $18$; both earlier bounds are those of the companion article hexagon:2611.00057. The first rests on two identities satisfied by every symmetric solution of odd size, one relating $v_2(C)$ to a difference of two products and one turning the index relation into an equality, together with an arithmetic…
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