In 9-11, prove each of the given statements, assuming that and n are integers with n>1 and that and .
for every integer (Use mathematical induction on m.)
The statement for all integers , by using mathematical induction on .
Let are integers with and that and .
The binomial expansion is:
To prove the statement , by using mathematical induction on .
In the above statement, are integers with .
It is given that, and .
Thus, there exist integers such that and .
Substitute 1 for in equation .
Thus, the statement is true for .
Let the statement is true for .
To prove the above statement for .
Substitute for in the above equation.
Use the binomial expansion in the above equation.
Simplify the above equation
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