Having problems with this question
n^3 - 7n + 3 is divisible by 3, for each integer n => 0.
---------------My work-------------------------
Show n is true for n = 0
0^3 -7(0) + 3 = 3
Then show n is true for n = K +1
(K + 1)^3 -7(k + 1) + 3 = k^3 + 3k^2 + 3k +1 - 7K -7 = k^3 + 3k^2 -4k -3
Im kinda stuck on how to proceed...
Induction tries to find out if the hypothesis being true for any n=k
causes the hypothesis to be true for n=k+1.
True for n=1 causes true for n=2
True for n=2 causes true for n=3
True for n=3 causes true for n=4 ...... to infinity.
Using k and k+1 examines this cause and effect in general.
If true for k causes true for k+1,
then we only need to examine the first n, as the hypothesis would then be true for all n.
So, if the formula is valid for some n=k,
and being valid for n=k causes validity for n=k+1,
you then only need to test the first term.
This is why you should write the k+1 expression containing the k expression.
If 3 does divide , then it will definately divide