I was wondering if someone can show me step by step on how to do this question:
Prove that for all integers n >= 1, 6|n (n^2 + 5)
So far I got the bases step for when n = 1.
I am having troubles with the induction step after n = 1.
No it's not a complete proof, as you have not shown that your final line is divisible by 6. In fact, you have not used your assumption at all.
Also, the writing of your base step is atrocious.
is a STATEMENT, that 6 divides . It can NOT be used in equations.
You would need to write something like
If then which is divisible by 6.