How to prove or disprove this statement:
For all $c, such that all conditions hold simultaneously:
- $z=is+i(i-1)/2-j-k(s+i+2j)-k(k-1)/2$,
- $z
and $0 - for all $0\leq m and $0
, a) holds
a) $ms+m(m-1)/2\neq is+i(i-1)/2-j-n(s+i+2j)-n(n-1)/2$
All variables are integers. I have tried computationally to find a counterexample but without luck.
This would imply the existence of several Self-avoiding walk on $\mathbb{Z}$ . (but not the converse.)