3 years ago

Sample 1: 64, 52, 72, 56, 80, 68, 75, 58, 48, 55

Mathematics

1 answer:

Blizzard [7]3 years ago

5 0

Answer: sample of 100

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Using fermat's little theorem, find the least positive residue of $2^{1000000}$ modulo 17.

torisob [31]

Fermat's little theorem states that
$a^p$ ≡a mod p

If we divide both sides by a, then
$a^{p-1}$ ≡1 mod p
=>
$a^{17-1}$ ≡1 mod 17
$a^{16}$ ≡1 mod 17

Rewrite
$a^{1000000}$ mod 17 as
$=(a^{16})^{62500}$ mod 17
and apply Fermat's little theorem
$=(1)^{62500}$ mod 17
=>
$=(1)$ mod 17

So we conclude that
$a^{1000000}$ ≡1 mod 17

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A circus tent is supported by a rope that is staked to the ground. The tent makes a 90 angle with the ground. The following visu

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<h3>Right-angled triangle</h3>

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