Fermat's Little Theorem examples

Find the least residue (modulo p) using Fermat's Little Theorem; or find the remainder when dividing by p. We start with a simple example, so that we can easily check the answer, then look at much bigger numbers where the answers cannot be directly checked on a calculator.
0:00 Fermat's Little Theorem: Least residue of a large number...
0:20 ...or: Remainder when dividing by a prime
0:50: Formula
1:50 Small Example
5:30 Big Example
8:40 Very Big Example

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[@MathsWithJay]

Thank you very much for your fabulous feedback.

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[@MathsWithJay]

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@Adrian Haro: Many thanks for this feedback

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Really

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Jay

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Jay

[@R1C4RD0R3D15]

Maths with Jay
I've been looking around for something particular, maybe you know the answer. How can you do this exact thing but without prime numbers? For example, Find the remainder of 9^342 | 10

[@MathsWithJay]

+Jake Moore This is a different situation, so think about it in a different way: Start by writing down the first few powers of 9, find the remainders when you divide by 10, and you will see a simple pattern...

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[@MathsWithJay]

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[@MathsWithJay]

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[@MathsWithJay]

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[@WelshGuitarDude]

Have i understood correctly here:
7^50 (mod 13)
Since 7^12 = 1 mod 13
50 = 4 * 12 + 2
So 7^50 = 7^(4*12+2)
= 1^4 * 7^2
= 1 * 49
= 10 mod 13
So least residue is 10 ?

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[@MathsWithJay]

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[@MathsWithJay]

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Maths with Jay 13 tears old. We do this topic in our enrichment work (early high school in Australia )

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@Nordin: Wow! That's impressive. I'm teaching this at a university. (By the way, in the UK, our year 7 students are 11 - 12 years old.)

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[@MathsWithJay]

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