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Vladimir [108]
3 years ago
9

Alyssa had 59 dollars to spend on 6 books. After buying them she had 11 dollars. How much did each book cost

Mathematics
1 answer:
Mrrafil [7]3 years ago
5 0
Answer: $20
Sandy had 138 dollars to spend on 6 books. After buying them she had 18 dollars. How much did each book cost? 20 dollars.
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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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