Question

- is this prove correct with math induction ?
-let a,b and n natural numbers from N,
a>=1,b>=1,n>=3
- n=a+b+1 - how may be prove it that always for any value of n will be one a and one b that this equation is true ?
- Assume there exists a natural number k such that k >= 3 and there exists a pair of natural numbers, a_k and b_k, such that (a_k + b_k + 1) = k.
Let a_(k+1) = a_k.
So, a_(k+1) is a natural number.
Let b_(k+1) = (b_k) + 1.
So, b_(k+1) is a natural number.
(a_(k+1) + b_(k+1) + 1) = [a_k + ((b_k) + 1) + 1] = [(a_k + b_k + 1) + 1] = (k + 1).
And (k + 1) is a natural number >= 3.
So,

Answer 1

No need induction. Just choose \(a=n-2\) and \(b=1\)