Tianak5996 Tianak5996
  • 03-03-2022
  • Mathematics
contestada

We can find a system of congruences where x≡a (mod 4) x≡b (mod 5) where the solution is x≡7 (mod 20).

Respuesta :

LammettHash
LammettHash LammettHash
  • 03-03-2022

If x ≡ 7 (mod 20), then

x ≡ 7 ≡ 27 ≡ 47 ≡ 67 ≡ 87 ≡ … (mod 20)

or equivalently, x = 7 + 20k for some integer k.

Taken mod 4, we have

x ≡ 7 + 20k ≡ 3 (mod 4)

and mod 5,

x ≡ 7 + 20k ≡ 2 (mod 5)

so that a = 3 and b = 2.

Answer Link

Otras preguntas

The Egyptian made many boats which were small and easily upset true or false
Which of the following statements about the U.S. and the Soviet Union is untrue? A. Their economic systems were different B. The had the same type of government
Help! The Council of Trent did all the following except approve the sale of indulgences reaffirm the authority of the Pope establish seminaries for the training
Javier drove 45 miles. This represents 60% of his entire trip. What is the total number of miles in Javier's trip?
Why did Richard Nixon resign as president?
Which best describes the function of the cell wall in cells? A. maintains the cell's nuclear structure B. moves materials within the cell C. supports the frame
solve for y=4x-300 and y=3x+600
What is the y intercept of y=|x+8|?
Clarify how intrapersonal conflict can lead to emotional stress
3x-5y=-6 -9x-5y=18 whats the answer