Question 1
Prove that \(7^n - 1\) is divisible by 6 for all \(n \in \mathbb{Z}^+\).
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Specialist Mathematics Β· Unit 3 Β· Mathematical induction and trigonometric proofs Β· Mathematical induction
Prove divisibility results for any positive integer π.
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Question 2
Use mathematical induction to prove that \(8^n - 3^n\) is divisible by 5 for all \(n \in \mathbb{Z}^+\).
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Question 3
Use mathematical induction to prove that \(5^n - 1\) is divisible by 4 for all positive integers \(n\).
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Question 4
Use mathematical induction to prove that \(5^n - 1\) is divisible by \(4\) for all \(n \in \mathbb{Z}^+\).
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