My favorite Fermat Little Theorem with Pascal Triangle

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

\boxed {m^{p} \equiv m \mod p}

When m = 2,

\boxed{2^{p} \equiv 2 \mod p}

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

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

1 \: 1 \implies sum = 2 = 2^1 \equiv 2 \mod 1

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

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)

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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