sprjeyaraman
sprjeyaraman sprjeyaraman
  • 18-08-2021
  • Mathematics
contestada

7 4K ≡ ________________ (mod 100 )
(a ) 4
(b ) 2
(c) 3
( d ) 1​

Respuesta :

guyshimshon guyshimshon
  • 18-08-2021
Not sure 74k is 74000 so mod 100 gives to digits from the right. So answer is 0.
Or it’s 7^4 = 2,401 so answer is 1.
Please check the question again
Answer Link
LammettHash
LammettHash LammettHash
  • 18-08-2021

I assume you're asked to find [tex]7^{4k}\pmod{100}[/tex] for positive integer k. To start, notice that

[tex]7^4 \equiv 7^3\times7 \equiv 343\times7 \equiv 43\times7 \equiv 301 \equiv 1\pmod{100}[/tex]

Then for every k, we have

[tex]7^{4k} \equiv (7^4)^k \equiv 1^k \equiv 1 \pmod{100}[/tex]

Answer Link

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