- 2 Fact Fn M Fn 1fm F Fm 1 Why Fix M By Induction On N 2 1 F X 1 M Fr M Fr 1 M By Definition Fr 1fm F F 1 (33.28 KiB) Viewed 15 times
2. Fact: Fn+m=Fn-1Fm+F Fm+1. Why: Fix m. By induction on n > 2: 1 F(x+1)+m = Fr+m+FR-1)+m (by definition) = FR-1Fm + F F
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2. Fact: Fn+m=Fn-1Fm+F Fm+1. Why: Fix m. By induction on n > 2: 1 F(x+1)+m = Fr+m+FR-1)+m (by definition) = FR-1Fm + F F
2. Fact: Fn+m=Fn-1Fm+F Fm+1. Why: Fix m. By induction on n > 2: 1 F(x+1)+m = Fr+m+FR-1)+m (by definition) = FR-1Fm + F Fm+1+Fx-2Fm+ FX-Fm+1 (induction hypothesis twice) = (FX-1 +Fx-2) Fm+ (Fx + FX-1) Fm+! (factoring) = F F. + Fk+1Fm+1 (by definition) 3. Fact: F. Find Why: Fix n. By induction on k > 1, and using item 2, Fk+1)n = Fxn+= Fin-1Fn+Fkn Fk+1 with Fkn divisible by Fr.
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