Question

If is any positive odd integer, then prove by induction that ( + ) ∣ ( + ). Hints: is positive odd i.e. = 2 + 1, where is any integer. Base case: start with = 1

Answer 1

Answer:

Since a and b are 2 positive integers

They can be expressed as a=2n+1;b=2m+1 where n,m are integers

So the expression

2

a+b

takes the form

2

2m+1+2n+1

2

2m+2n+2

m+n+1

Since m.n are integers m+n+1 is also a integer

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