How to prove or disprove this statement:
For all $c 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.)