Prove by induction that 8n1 is divisible by 7 for all integers n1-.pdf
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For any integer n ≥ 1, 8n - 1 is divisible by 7. The base case of n = 1 shows that 8 - 1 = 7 is divisible by 7. Assuming 8k - 1 is divisible by 7, 8(k + 1) - 1 can be written as 8k - 1 + 8, which is divisible by 7 since both terms are divisible by 7. Therefore, by mathematical induction, 8n - 1 is divisible by 7 for all integers n ≥ 1.
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