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

Expert Solution

Colby Messinger answered 1 year ago

Let x, y ∈ Z. Prove that x ≡ y + 1 (mod 2) if and...

Let x, y ∈ Z. Prove that x ≡ y + 1 (mod 2) if and only if x ≡ y + 1 (mod 4) or x ≡ y + 3 (mod 4)

Mystery(y, z: positive integer) 1 x=0 2 while z > 0 3 if z mod 2...

Mystery(y, z: positive integer) 1 x=0 2 while z > 0 3 if z mod 2 ==1 then 4 x = x + y 5 y = 2y 6 z = floor(z/2) //floor is the rounding down operation 7 return x Simulate this algorithm for y=4 and z=7 and answer the following questions: (3 points) At the end of the first execution of the while loop, x=_____, y=______ and z=_______. (3 points) At the end of the second execution of...

Use the Pohlig-Hellman algorithm to solve 19x ≡ 184 (mod 337) for x. Write out at...

Use the Pohlig-Hellman algorithm to solve 19x ≡ 184 (mod 337) for x. Write out at least one successive squaring in detail, and at least one instance of the Chinese Remainder Theorem.

Find all solutions of the equation x^{5}=2

*(1)(a) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z):...

*(1)(a) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): z=c}. (b) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): x=a}. (c) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): y=b}. *(2) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): z=kx+b} assuming both b and k are positive. (a) For what value of...

0 mod 35 = 〈0 mod 5, 0 mod 7〉 12 mod 35 = 〈2 mod...

0 mod 35 = 〈0 mod 5, 0 mod 7〉 12 mod 35 = 〈2 mod 5, 5 mod 7〉 24 mod 35 = 〈4 mod 5, 3 mod 7〉 1 mod 35 = 〈1 mod 5, 1 mod 7〉 13 mod 35 = 〈3 mod 5, 6 mod 7〉 25 mod 35 = 〈0 mod 5, 4 mod 7〉 2 mod 35 = 〈2 mod 5, 2 mod 7〉 14 mod 35 = 〈4 mod 5, 0 mod 7〉...

Find the volume of the solid bounded by the surface z =5 +(x-4) ^2+2y and the...

Find the volume of the solid bounded by the surface z =5 +(x-4) ^2+2y and the planes x = 3, y = 3 and coordinate planes. a. First find the volume by actual calculation. b. Estimate the volume by dividing the region into nine equal squares and evaluating the functional value at the mid-point of the respective squares and multiplying with the area and summing it. Find the error from step a. c. Then estimate the volume by dividing each...

Find the volume of D= {(x,y,z): x^2+y^2+z^2<_ 4, x _>0, y_>0

Given function f(x,y,z)=x^(2)+2y^(2)+z^(2), subject to two constraints x+y+z=6 and x-2y+z=0. find the extreme value of f(x,y,z)...

Given function f(x,y,z)=x^(2)+2*y^(2)+z^(2), subject to two constraints x+y+z=6 and x-2*y+z=0. find the extreme value of f(x,y,z) and determine whether it is maximum of minimum.

Find the maximum and minimum of the function f(x, y, z) = (x^2)(y^2)z in the region...

Find the maximum and minimum of the function f(x, y, z) = (x^2)(y^2)z in the region D = {(x, y, z)|x^2 + 2y^2 + 3z^2 ≤ 1}.

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