taylortaylor8664 taylortaylor8664
  • 21-09-2019
  • Mathematics
contestada

For a-b, reduce to the least non-negative residue

a. (88 · 95 · 36 · 703) mod 7

b. 4^(83) mod 11

Respuesta :

sqdancefan
sqdancefan sqdancefan
  • 21-09-2019

Answer:

  a.  6

  b.  9

Step-by-step explanation:

a. The product modulo 7 can be found from the product of the individual numbers modulo 7:

  (88·95·36·702) mod 7 = (88 mod 7)·(95 mod 7)·(36 mod 7)·(703 mod 7) mod 7

  = (4·4·1·3) mod 7 = 48 mod 7 = 6

__

b. Powers of 4 mod 11 repeat with period 5:

  4 mod 11 = 4

  4^2 mod 11 = 5

  4^3 mod 11 = 9

  4^4 mod 11 = 3

  4^5 mod 11 = 1

So, 4^83 mod 11 = 4^3 mod 11 = 9

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