Prove that (5^2n) - 1 is a multiple of 8 for all natural numbers. (By induction)
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Originally Posted by bearej50 Prove that (5^2n) - 1 is a multiple of 8 for all natural numbers. (By induction) .....Here is the main part Let 5^2k-1 is a multiple of 8 so 5^{2k}-1 =8 m [ m is any integer] 5^2k = 8m+1 For(k+1) $\displaystyle 5^{2(k+1)}-1$ $\displaystyle =25*5^{2k}-1$ $\displaystyle =25*(8m+1)-1 $ $\displaystyle =25*8m+24$ $\displaystyle =8(25m+3)$
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