49-52 Proving a statement Show that the given statement is true.
Prove that is an integer for all and for .[Suggestion: Use induction to show that the statement is true for all n, and use Exercise 53 for the induction step.]
is an integer for all and for .
1. is an integer for .
2. If is an integer for , then is an integer for as well.
Here, and are positive integers.
Since , then or .
Thus, is an integer.
The statement is true for
Let the statement is true for , then
is an integer for and for
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