ktseng26
Answered

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What is the remainder when $2^3 \cdot 4^5 \cdot 6^7 \cdot 8^9$ is divided by 13?

Sagot :

madisoneilts28

Answer:Hint:

the remainder is 2.

Step-by-step explanation:

23≡1 mod 7 and 33≡−1 mod 7.

Edit: The only thing you need from the modular arithmetic is that

a⋅b mod 7=(a mod 7)(b mod 7) mod 7,

meaning the remainder of a product is the remainder of the product of remainders. This is self-evident as a⋅b must have the same remainder as (a−7k)⋅(b−7l).

Since exponentiation is just repeated multiplication, we can write

230⋅320=(23)10⋅(33)6⋅32≡110⋅(−1)6⋅9=9

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