Prove that there are no integers x, y such that x + y = 200 and greatest common divisor of x and y is 7.

The greatest common divisor of 7 and 18 is

If p is prime and x is not divisible by p, then find the greatest common divisor of p and x is

Check whether the following statement is true or false by proving its contrapositive. 'If x,y are integers such that xy is odd, then both x and y are odd integers'.

Write the converse of each of the following conditional statements : If x and y are two integers such that (x -y) is always a positive integer , then xgty .

Prove that the radii of circles x^2 + y^2 = 1, x^2 + y^2 - 2x -6y = 6 and x^2 + y^2 - 4x - 12y = 9 are in A.p.

Complex numbers whose real and imaginary parts x and y are integers and satisfy the equation 3x^(2)-|xy|-2y^(2)+7=0 , Find the value of x and y .

Prove that (sin (x +y) )/( sin (x-y)) = (tan x + tan y)/( tan x - tan y).

Prove that the greatest value of x y is c^3/sqrt(2a b) , if a^2x^4+b^2y^4=c^6dot

Let f(x) = ([x]+1)/({x}+1) for f: [0, (5)/(2) ) to ((1)/(2) , 3] , where [*] represents the greatest integer function and {*} represents the fractional part of x. Draw the graph of y= f(x) . Prove that y=f(x) is bijective. Also find the range of the function.

Prove that the focal distance of the point (x ,y) on the parabola x^2-8x+16 y=0 is |y-5|