# Mathematical induction

1. Oct 17, 2007

### kring_c14

1. The problem statement, all variables and given/known data

n $$\epsilon$$$$N$$=n$$\geq0$$
6 divides (n$$^{3}$$+5n)

2. Relevant equations
(n$$^{3}$$+5n)=6q

3. The attempt at a solution
by expanding and simplifying and later on substituting 6q in
(n+1)$$^{}3$$+5(n+1)

ive arrived at 6q+3n$$^{}2$$ +3n+6

then.. im stuck...pls help...lot of thanks!

2. Oct 17, 2007

### kring_c14

i tried multiplying and dividing it by two so that the 6 would be factored out...ive got fractions..its supposed to be whole numbers

3. Oct 18, 2007

(n+1)^3 +5(n+1)
n^3 + 3n^2 + 3n + 1 + 5n + 5
(n^3 + 5n) + 3n^2 + 3n + 6
6q + 3n^2 + 3n + 6
This reduces the problem down to proving that 3n^2 + 3n + 6 is a multiple of 6

3(n^2 + n + 2)
Now you just have to prove that n^2 + n + 2 is a multiple of 2, (is even).

Last edited: Oct 18, 2007