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

lets help find the answer
Is North Korea a capitalist country
A meaningful sentence with barber and numb in one sentence
TRUE or FALSE: HTML is used to style web pages.
Someone help dont scam or you get report. :)
Which of the following element has the highest ionization energy? O A. CI OB. I O C. F O D. Br
A rectangular prism has a length of 9 inches, a width of 6 inches, and a height of 7 inches. What is the volume of the rectangular prism? Use the formula V = lw
A woodworker is creating arms for a bench. If the helght of the bench's back is 3 feet tall and the width of the bench's seat Is 1 foot long, what is the length
Can someone help me please
The data below shows the grams of fat for a variety of snacks. Morris wants to calculate the standard error of the sample mean for this set of data. Snack Grams