My favorite Fermat Little Theorem with Pascal Triangle

Math Online Tom Circle

Fermat Little Theorem: For any prime integer p, any integer m

$latex boxed {m^{p} equiv m mod p} &s=3$

When m = 2,

$latex boxed{2^{p} equiv 2 mod p}&fg=aa0000$

Note: 九章算数 Fermat Little Theorem (m=2)

Pascal Triangle (1653 AD France )= (杨辉三角 1238 AD – 1298 AD)

$latex 1 : 1 implies sum = 2 = 2^1 equiv 2 mod 1$

$latex 1: 2 :1implies sum = 4 = 2^2 equiv 2 mod 2 ;(equiv 0 mod 2)$

$latex 1 :3 :3 :1 implies sum = 8= 2^3 equiv 2 mod 3$

1 4 6 4 1 => sum = 16= 2^4 (4 is non-prime)

$latex 1 :5 :10: 10: 5: 1 implies sum = 32= 2^5 equiv 2 mod 5$

[PODCAST]

https://kpknudson.com/my-favorite-theorem/2017/9/13/episode-4-jordan-ellenberg

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