I am trying to prove that 3 divides [tex]n^3~-7n+3[/tex] for all integers n greater than or equal to 0. I have gotten to this point: [tex]3|(k~+~1)^3~-~7(k~+~1)~+~3[/tex] Where I try to show that is true for k+1. I have been scribbling on scrap paper trying to figure it out. I've expanded the expression countless times no avail. Could someone give me a hint?