How many pairs of positive integers x, y exist such that HCF of x, y = 35 and sum of x and y = 1085?

Q) The number ofpositive integer pairs (x, y) such that 1/x+1/y=1/2007 , x < y is

Let R be a relation on the set A of ordered pairs of positive integers defined by (x , y) R (u , v) if and only if x v = y u . Show that R is an equivalence relation.

The number of pairs of positive integers (x,y) where x and y are prime numbers and x^(2)-2y^(2)=1 , is

If x and y are positive integers such that tan^(-1)x+cot^(-1)y=tan^(-1)3 , then:

Find two positive numbers x and y such that their sum is 35 and the product x^2y^5 is a maximum.

If x,y and z are positive integers such that x < y < z and x + y + z = 6 , then what is the value of z?

If x and y are positive integers and sqrt(x) = y + 3 ,then what is the value of y^(2) ?

Let R be a relation on the set A of ordered pairs of positive integers defined by (x , y)"R"(u , v) if and only if x v=y u . Show that R is an equivalence relation.

If x and y are two positive integers and x + y = 5 , then what is the probability that x equal 1 ?

If x and y are positive integers and (2x +y) is even, which of the following must be even ?