Determine the solution of the following equation mod N. 1.7x≡2 mod 15, where N= 15 2.x≡8...

Determine the solution of the following equation mod N.

1.7x≡2 mod 15, where N= 15

2.x≡8 mod 11, x≡3 mod 19, where N= 209

3.x≡2 mod 7, x≡2 mod 11, x≡1 mod 13, where= 1001

Expert Solution

Solve each problem step by step. Before start reading make sure you have concepts about linear congruence and their basic properties.

Colby Messinger answered 1 year ago

1. Determine forced and natural response for the following equation, where y[-1] =1, y[-2]=1 and x[n]...

1. Determine forced and natural response for the following equation, where y[-1] =1, y[-2]=1 and x[n] = delta[n]. y[n]+1/2 y[n-1] -1/4 y[n-2] = x[n] 2. find the impulse response of the system described below y[n]=1/2 y[n-1] + 2x[n]

A 5th filter is described by the difference equation: 2y(n)=2 x(n)+7 x(n-1)+3 x(n-2)-8 x(n-3)+ x(n-4)-8 x(n-5)+7...

A 5th filter is described by the difference equation: 2y(n)=2 x(n)+7 x(n-1)+3 x(n-2)-8 x(n-3)+ x(n-4)-8 x(n-5)+7 y(n-1)-3 y(n-2)+5y(n-3)- y(n-4) Determine the frequency response. Plot the magnitude and the phase response of this filter. Consider the plot -π≤w≤π for 501 points. Describe the magnitude response (Low pass filter, High Pass filter, etc.) Determine the system stability. Determine the impulse response h(n). You may set the period to -100≤n≤100 Determine the unit step response for -100≤n≤100 . (Matlab)

Find the series solution of the following equation x(d^2y/dx^2+(1-x)dy/dx+ny=0. where n=0,1,2

Show that x^8 ≡ 2 ( mod 13) has no solutions.

Solve the following system of congruences: x ≡ 2 (mod 14) x ≡ 16 (mod 21)...

Solve the following system of congruences: x ≡ 2 (mod 14) x ≡ 16 (mod 21) x ≡ 10 (mod 30)

Prove the following theorem. If n is a positive integer such that n ≡ 2 (mod...

Prove the following theorem. If n is a positive integer such that n ≡ 2 (mod 4) or n ≡ 3 (mod 4), then n is not a perfect square.

1. Use backward substitution to solve: x=8 (mod 11) x=3 (mod 19)

1. Use backward substitution to solve: x=8 (mod 11) x=3 (mod 19) 2. Fine the subgroup of Z24 (the operation is addition) generates by the element 20. 3. Find the order of the element 5 in (z/7z)

Find all x ∈ Z such that x≡2 mod 221 and x≡5 mod 184.

let p = 1031, Find the number of solutions to the equation x^2 -2 y^2=1 (mod...

let p = 1031, Find the number of solutions to the equation x^2 -2 y^2=1 (mod p), i.e., the number of elements (x,y), x,y=0,1,...,p-1, which satisfy x^2 - 2 y^2=1 (mod p)

1- Find the solution of the following equations. For each equation, 2- determine the type of...

1- Find the solution of the following equations. For each equation, 2- determine the type of the category that the equation belongs to. Separable equation, Homogenous equation, Linear equation, or Bernolli equation? 1. ydx − x ln xdy = 0 2. y ′ = (1+y^2) / (xy(1+x2)) 3. xy′ + (1 + y^2 ) tan^−1 y = 0 4. y ′ = (y) / (x+ √xy) 5. y ′ = (y−x) / (y+x) 6. tan x dy/dx + y =...

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