In the inductive step, add and subtract by a certain multiple of 6 in order to use the inductive hypothesis.
Preciousj B.
Can you give the solution in that problem
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10/16/22
Scott F.
tutor
We take as the inductive hypothesis that 5 divides 6^n + 4 for some natural number n. We need to show that 5 divides 6^(n+1) + 4 using the hypothesis to complete the induction. We'd like to factor a 6 from 6^(n+1) to have 6^n somewhere, but this would give us 6^(n+1) + 4 = 6(6^n) + 4 which isn't that helpful yet. Nowhere in this new expression can we use the fact that 6^n + 4 is divisible by 5. If we add 4 within the parentheses, we'd get 6(6^n + 4) + 4, but this would be changing the expression. So we have to subtract 6x4=24 from the expression, giving us that 6^(n+1) + 4 = 6(6^n + 4) - 24 + 4. From here we can use the inductive hypothesis and conclude. Does this help?
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10/16/22
Preciousj B.
Can you arrange it?
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10/16/22
Preciousj B.
I don't understand10/16/22