- #1
johnnyICON
- 79
- 0
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?
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?