Yahoo Answers: Answers and Comments for Mathematical Induction? [Mathematics]
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Tue, 19 Nov 2019 20:30:22 +0000
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Yahoo Answers: Answers and Comments for Mathematical Induction? [Mathematics]
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https://answers.yahoo.com/question/index?qid=20191119203022AAGhxX7
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From Φ² = Φ+1: a  b equals and so is a factor of a¹  b¹.
If...
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https://answers.yahoo.com/question/index?qid=20191119203022AAGhxX7
Tue, 19 Nov 2019 21:30:40 +0000
a  b equals and so is a factor of a¹  b¹.
If a  b is a factor of aᵏ  bᵏ, so aᵏ  bᵏ = C(a  b), then
aᵏ⁺¹  bᵏ⁺¹ = aaᵏ  bbᵏ
aᵏ⁺¹  bᵏ⁺¹ = aaᵏ  abᵏ + abᵏ  bbᵏ
aᵏ⁺¹  bᵏ⁺¹ = a(aᵏ  bᵏ) + (a  b)bᵏ
aᵏ⁺¹  bᵏ⁺¹ = a(a  b)C + (a  b)bᵏ
aᵏ⁺¹  bᵏ⁺¹ = (a  b)(aC + bᵏ)
So a  b is a factor of aᵏ⁺¹  bᵏ⁺¹ if it is a factor of aᵏ  bᵏ,
and a  b is a factor of a¹  b¹,
thus a  b is a factor of aⁿ  bⁿ for Integer n > 0.

From ted s: true if n = 1...assume true for n = k..ie . a^...
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https://answers.yahoo.com/question/index?qid=20191119203022AAGhxX7
Tue, 19 Nov 2019 21:01:21 +0000
true if n = 1...assume true for n = k..ie . a^k  b^k = ( a  b ) W...then
a^(k+1)  b^(k + 1 ) = a^(k+1)  a b^k + a b^k  b^(k+1) ≡a(a^k  b^k) + b^k ( a  b)
= a (ab)W +b^k ( a  b) = (a  b ) ( a W + b^k)

From Star Butterfly: Prove by mathematical induction that a  b is ...
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https://answers.yahoo.com/question/index?qid=20191119203022AAGhxX7
Tue, 19 Nov 2019 20:30:33 +0000
Prove by mathematical induction that a  b is a factor of a^n  b^n.