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st1 is insuff: consider p=0 (then m=1) and p=2 (then m=2)
st2 is suff: if (p^3)<-1 then p<-1
then m=-p+(-2)^p. -p is at least 2 (because p is an integer less than -1) and (-2)^p is always between -1 and 1 ... so m will be at least 1 and m^3>1 as well. sufficient