Proof by Induction Use mathematical induction to show that the given statement is true.
The Fibonacci number is divisible by for all natural numbers .
The Fibonacci number is divisible by using mathematical induction.
The Fibonacci number is given as,
Prove basic step for . Assume the statement is true for some natural number and show that the statement is true for .
Denote the statement “The Fibonacci number is divisible by ” by .
This proves Step .
Assume is true for some . This is called the induction hypothesis.
Show that is true.
Since induction hypothesis is true hence is divisible by and can be written as for some integer
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