(1) a^3-3a=b(2) b^3-3b=c(3) c^3-3c=a(4) a<=b<=c

from 3,4 we getc^3-3c<=cc^3<=4cc^2<=4since c>0 thenc<=2

from 1,4 we havea^3-3a>=aa^3>=4aa^2>=4since a>0 thena>=2and since the smallest a can be is 2, and the largest c can beis 2 and a<=c then we have a=c=2 and that makes b=2

thus the only solution is (2,2,2)

blackjack

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