The characteristic equation is
It has solutions
Use the initial conditions to solve:
Solve the system and get
Therefore, we have:
Now, perhaps you can use this to prove the solutions are always odd.
I'm not sure how to go about setting up the steps for this problem.
a1 = 1, a2 = 1 and an = 2an-1 + an-2 for all n ≥ 3. prove an is odd for all n≥1.
first six are 1,1,3,7,17,41
I could also use help on another problem...
proving (3,5,7) is the only prime triple - consecutive odd integers which are all prime -
to do this i prove that for any odd integer k, one of the integers 2k+1, 2k+3, and 2k+5 must be divisible by 3.
I know i need to use cases for this.
how does this then show that (3,5,7) is the only prime triple?
thanks for the input guys.