Proof by Induction question | Mathematics | Page 1

dusky torrentBOT Mar 18, 2025, 6:56 AM

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native wraith Mar 18, 2025, 8:07 AM

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LHS? What is that? (I'm from Italy)

stiff bone Mar 18, 2025, 9:27 AM

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It would be so much easier if you could just use congruences

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I think I got it
Replace 2^(4k + 3) by 11m - 3^(3k + 1) in the last part

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And you get :
= 16 * (11m - 3^(3k + 1)) + 27 * 3^(3k + 1) = 11*(16m) + (27 - 16)*3^(3k + 1) = 11*(16m + 3^(3k + 1))

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Which is obviously divisible by 11

oblique breach Mar 18, 2025, 10:40 AM

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Next step is 3^3=11+2^4.

#Proof by Induction question