$\"\"$

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Statement : $\"\"$ is divisible by $\"\"$ .

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The statement is True.

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Proof :

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Let $\"\"$ be the statement $\"\"$ is divisible by $\"\"$ .

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$\"\"$ is the statement that $\"\"$ is divisible by $\"\"$ , $\"\"$ is true since

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$\"\"$ which is divisible by $\"\"$ .

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Assume $\"\"$ is true where $\"\"$ is a positive integer and we have to prove that $\"\"$ must be

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true i.e., show that $\"\"$ for some integer $\"\"$ implies that

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$\"\"$ is divisible by $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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Multiply each side by $\"\"$ .

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$\"\"$

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Because $\"\"$ and $\"\"$ are integers $\"\"$ is an integer and $\"\"$ is divisible by $\"\"$ .

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Because $\"\"$ is true for $\"\"$ and $\"\"$ implies $\"\"$ .

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$\"\"$ is true for $\"\"$ and so on.

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By the principle of mathematical induction $\"\"$ is divisible by $\"\"$ for all positive

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integers of $\"\"$ .

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$\"\"$

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By the principle of mathematical induction $\"\"$ is divisible by $\"\"$ for all positive

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integers of $\"\"$ .