Number Theory | Fermat's Little Theorem Example 1

We give a few examples of applications of Fermat's Little Theorem.

[Abhisruta]

In the last part of example 2, you could have reused FLT to draw that 2^20 \equiv 4.2^18 \equiv 4 (mod 19).

Series of great videos. Loved it...

[georgesadler]

Professor M. Penn, thank you for the application to Fermat Little Theorem.

[amarsinha]

Sir very nice and supportive for my exam thank a lot you sir

[petersievert]

Wow, watching this today after having consumed everything of last 12 months really feels like time and space travelling :-)

[GrimAxel]

Another thing to note would be that 10^k (k in Z) mod 18 will always be 10. So n^(10^k) mod 19 will be congruent to n^10 mod 19 for all n where gcd(n, 19)=1.

[keithmasumoto]

5^10=1(mod11) because: 5^2=25=3(mod11) and we need 5 of these because 5^10=(5^2)^5. So we end up with 3^5 which is easy to see as 243. Divide by 11 and you get 22 remainder 1, our desired result.

[datsmydab-minecraft-and-mo]

how would you go about things if the guy in the exponent was less that n where n corresponds to the number in mod n ?

[PunmasterSTP]

Little theorem? More like lit theorem, because it's awesome!