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# Strong Induction and the Fibonacci Numbers

## Lecture no. 13 from the course: Prove It: The Art of Mathematical Argument

Taught by Professor Bruce H. Edwards | 30 min | Categories: The Great Courses Plus Online Mathematics Courses

Use a technique called strong induction to prove an elementary theorem about prime numbers. Next, apply strong induction to the famous Fibonacci sequence, verifying the Binet formula, which can specify any number in the sequence. Test the formula by finding the 21-digit-long 100th Fibonacci number.

## 24 Lectures

1

What Are Proofs, and How Do I Do Them?

0 of 31 min

2

The Root of Proof—A Brief Look at Geometry

0 of 30 min

3

The Building Blocks—Introduction to Logic

0 of 30 min

4

More Blocks—Negations and Implications

0 of 30 min

5

Existence and Uniqueness—Quantifiers

0 of 30 min

6

The Simplest Road—Direct Proofs

0 of 30 min

7

Let’s Go Backward—Proofs by Contradiction

0 of 30 min

8

Let’s Go Both Ways—If-and-Only-If Proofs

0 of 31 min

9

The Language of Mathematics—Set Theory

0 of 30 min

10

Bigger and Bigger Sets—Infinite Sets

0 of 32 min

11

Mathematical Induction

0 of 30 min

12

Deeper and Deeper—More Induction

0 of 31 min

13

Strong Induction and the Fibonacci Numbers

0 of 30 min

14

I Exist Therefore I Am—Existence Proofs

0 of 31 min

15

I Am One of a Kind—Uniqueness Proofs

0 of 30 min

16

Let Me Count the Ways—Enumeration Proofs

0 of 31 min

17

Not True! Counterexamples and Paradoxes

0 of 29 min

18

When 1 = 2—False Proofs

0 of 31 min

19

A Picture Says It All—Visual Proofs

0 of 31 min

20

The Queen of Mathematics—Number Theory

0 of 28 min

21

Primal Studies—More Number Theory

0 of 31 min

22

Fun with Triangular and Square Numbers

0 of 30 min

23

Perfect Numbers and Mersenne Primes

0 of 30 min

24

Let’s Wrap It Up—The Number e

0 of 31 min

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