Understanding Lucas-Carmichael Numbers

The video introduces Lucas-Carmichael numbers, named after Édouard Lucas and Robert Daniel Carmichael. These are composite numbers where each prime factor plus one is also a factor of the number plus one. Examples include 399, 935, and 2015, illustrating the concept. The video highlights the rarity of these numbers and concludes with acknowledgments to supporters.

Who are the mathematicians after whom Lucas-Carmichael numbers are named?

• Pythagoras and Euclid

• Carl Friedrich Gauss and Leonhard Euler

• Isaac Newton and Albert Einstein

• Édouard Lucas and Robert Daniel Carmichael

What is the defining condition for a number to be a Lucas-Carmichael number?

• It must be a perfect square.

• It must be an even number.

• p+1 must be a factor of n+1.

• It must be a prime number.

What is the smallest Lucas-Carmichael number?

• 1000

• 399

• 100

• 500

Which of the following is a prime factor of 399?

• 11

• 5

• 13

• 3

When 1 is added to the prime factors of 399, which of the following is a factor of 400?

• 8

• 10

• 12

• 9

What are the prime factors of 935?

• 7, 11, 23

• 5, 11, 17

• 3, 7, 19

• 2, 5, 13

After adding 1 to the prime factors of 935, which of the following is a factor of 936?

• 15

• 18

• 20

• 22

What is the smallest Lucas-Carmichael number with 5 factors?

• 935

• 2015

• 399

• 588455

How common are Lucas-Carmichael numbers?

• Very common

• Rare

• Every number is a Lucas-Carmichael number

• Only even numbers are Lucas-Carmichael numbers

What is the collaboration mentioned in the video?

• Numberphile and the Royal Society

• Numberphile and NASA

• Numberphile and the Mathematical Sciences Research Institute

• Numberphile and CERN