Let x and y be integers such that 17 | (3x +5y). Prove that 17 |...

Let x and y be integers such that 17 | (3x +5y). Prove that 17 | (8x + 19y).

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Colby Messinger answered 2 years ago

Let x and y be integers. Prove that if x^2 + y^2 is a multiple of...

Let x and y be integers. Prove that if x^2 + y^2 is a multiple of 7, then x and y are both multiples of 7.

Let x, y be integers, and n be a natural number. Prove that x ^(2n) −...

Let x, y be integers, and n be a natural number. Prove that x ^(2n) − y ^(2n) is divisible by x + y

Proof of If and Only if (IFF) and Contrapositive Let x,y be integers. Prove that the...

Proof of If and Only if (IFF) and Contrapositive Let x,y be integers. Prove that the product xy is odd if and only if x and y are both odd integers. Proof by Contradiction Use proof by contradiction to show that the difference of any irrational number and any rational number is irrational. In other words, prove that if a is irrational and b is a rational numbers, then a−b is irrational. Direct Proof Using a direct proof, prove that:...

Solve the set of equations: 3x - 5y = - 1, x - y = - 1?

Calculate the all of the second order derivatives of f(x,y)=x^4 y- 〖3x〗^4 y^3+5y-10 Let be f(x,y,x)=2x^5...

Calculate the all of the second order derivatives of f(x,y)=x^4 y- 〖3x〗^4 y^3+5y-10 Let be f(x,y,x)=2x^5 yz^3-3x^(-4) y^3 calculate the f_xyz=? If f(x,y,z)〖=5e〗^(-xyz^6 ) +lnx calculate the f_yxz=? Let f(x,y)=cos(x^3 y) ise df/dx=? df/dy=? z=2x+y , x=sin(3t ) and y=cos(3t) using the chain rule calculate the dz/dt where t=π/2. Find the critical points of the f(x,y)=〖6x〗^2+12y^2+12x-24y and provide the information about the critical points obtained (if it is max, min or saddle point).

let f(x,y)=x^2y(2-x+y^2)-4x^2(1+x+y)^7+x^3y^2(1-3x-y)^8 find the coefficient of x^5y^3

. Let x, y ∈ R \ {0}. Prove that if x < x^(−1) < y...

. Let x, y ∈ R \ {0}. Prove that if x < x^(−1) < y < y^(−1) then x < −1.

Prove for the system of ordinary differential equations x'=-x, and y'=-5y the origin is lyapunov stable,...

Prove for the system of ordinary differential equations x'=-x, and y'=-5y the origin is lyapunov stable, attracting and asymptotically stable using the EPSILON DELTA definition of each. The epsilon and delta that make the definitions hold must be found.

x' = -3x + 2y, y' = -10x + 5y +2e^t/cos 2t Solve the system by...

x' = -3x + 2y, y' = -10x + 5y +2e^t/cos 2t Solve the system by variation of parameters

Let X and Y be T2-space. Prove that X*Y is also T2

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