Understanding Brown Numbers and Conjectures

Professor Ed Copeland introduces Brown numbers, a pair of integers m and n such that n factorial plus 1 equals m squared. He provides examples and discusses the conjecture by mathematician Paul Erdos, who suggested there are only three such pairs. The video also explores what makes a conjecture credible, emphasizing the need for it to hold in numerous situations and survive obvious tests, though a formal proof is required for complete validation.

What is the defining property of Brown numbers?

• m factorial plus 1 equals n squared

• n factorial plus 1 equals m squared

• m factorial equals n squared

• n factorial equals m squared

What is the relationship between n factorial and m squared in Brown numbers?

• n factorial is less than m squared

• n factorial plus 1 equals m squared

• n factorial is greater than m squared

• n factorial minus 1 equals m squared

Which of the following is a pair of Brown numbers?

• (6, 3)

• (8, 5)

• (3, 2)

• (5, 4)

What is the result of 5 factorial plus 1?

• 49

• 36

• 121

• 25

According to Paul Erdos, how many Brown numbers are there?

• Four

• Three

• Two

• Five

What is a notable aspect of Paul Erdos's lifestyle?

• He was a traveling mathematician

• He was a famous artist

• He worked alone

• He lived in a mansion

What phrase would Erdos use when visiting collaborators?

• Do you have time?

• Is your mind open?

• Are you ready to work?

• Let's solve problems

What is required for a conjecture to be credible?

• It must be simple

• It must be widely accepted

• It must be tested in many situations

• It must be proven

Why can't we test a conjecture for an infinite number of cases?

• It's too expensive

• It's not practical

• It's unnecessary

• It's impossible

What does a formal proof provide for a conjecture?

• A suggestion

• A validation

• A theory

• A hypothesis