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Problem: Use the strong induction to establish that for all $n\ge1$ $a^n-1 = (a-1)(a^{n-1}+a^{n-2}+a^{n-3}+\cdots+a+1)$. [Hint: $a^{n+1}-1=(a+1)(a^n-1)-a(a^{n-1}-1)$].
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Sun, 31 Jan 2021 12:55 GMT