No, not that boring stuff you had to suffer through in high school. We’re talking about the real deal Fermat’s Little Theorem (FLT)! This baby is so cool and easy to understand that even your grandma could get it.

So what exactly is FLT? Well, let me put it this way: imagine you have a group of friends who all love pizza. You decide to order 10 pizzas for the gang, but only one person can eat each pizza. How many people do you need in your group to ensure that everyone gets a slice?

If you said “10,” then congratulations! You’ve just applied FLT without even realizing it. The theorem states that if p is a prime number and a is any integer not divisible by p, then the remainder when a^(p-1) is divided by p is always 1.

Let me break that down for you: let’s say your friend group has 25 people in it (which is way too many for pizza night, but bear with me). You want to make sure everyone gets a slice of the 10 pizzas. Since there are only 10 slices and 25 people, some will have to share or go without. But if you use FLT, you can ensure that each person gets at least one slice!

Here’s how: let’s say your friend’s name is Sarah (because who doesn’t love a good pizza-loving Sarah?). Her lucky number is 17, which isn’t divisible by the prime number p of 25. So we can use FLT to calculate whether or not she gets a slice:

a = 17
p = 25 (the total number of people)
(17^(24)) % 25 = 13

So Sarah’s remainder when 17 is raised to the power of 24 and then divided by 25 is 13. This means that if we divide the pizzas evenly among all 25 people, Sarah will get a slice (because her remainder is not zero). And since this works for every person in your group, you can be sure that everyone gets at least one slice!

Now, I know what some of you are thinking: “But wait, isn’t FLT just an overcomplicated way to calculate remainders? Can’t we just do it the old-fashioned way?” And my answer is… yes. But where’s the fun in that?! Plus, using FLT can actually save us time and effort when dealing with large numbers or complex calculations.

And if she doesn’t believe me, just invite her over for pizza night and let FLT do the work.