Proving a Factorization Show that is a factor of for all natural numbers .
is a factor of for all natural numbers .
Principal of Mathematical Induction:
Suppose is a statement depending on every natural number and the following conditions are satisfied.
For every natural number , if is true then is true.
Then is true for every natural number .
Suppose denote the statement is a factor of .
is a factor of . …
Step Show that is true.
Substitute for in equation .
is a factor of .
This implies that is true.
Step Assume that is true.
So, is divisible by
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