The number of positive integral ordered pairs of `(a ,b)` such that `6,a ,b` are in harmonic progression is _________.

The number of positive integral solutions of the equation xyz = 30 is

Find the number of positive integral solutions of x y z=21600.

Find the number of positive integral solutions of the equation x+y+z=12.

The number of positive integral solutions of the equation x + y + z = 100 is

The number of positive integral solutions of x^4-y^4=3789108 is a. 0 b. 1 c. 2 d. 4

Statement 1: The number of positive integral solutions of a b c=30 is 27. Statement 2: Number of ways in which three prizes can be distributed among three persons is 3^3

Find the total number of positive integral solutions for (x ,y ,z) such that x y z=24. Also find out the total number of integral solutions.

Let a ,b be positive real numbers. If a A_1, A_2, b be are in arithmetic progression a ,G_1, G_2, b are in geometric progression, and a ,H_1, H_2, b are in harmonic progression, show that (G_1G_2)/(H_1H_2)=(A_1+A_2)/(H_1+H_2)=((2a+b)(a+2b))/(9a b)

Let a ,b be positive real numbers. If a A_1, A_2, b be are in arithmetic progression a ,G_1, G_2, b are in geometric progression, and a ,H_1, H_2, b are in harmonic progression, show that (G_1G_2)/(H_1H_2)=(A_1+A_2)/(H_1+H_2)=((2a+b)(a+2b))/(9a b)

Number of ordered pairs (s) , (a,b) of real numbers such that (a+ib)^(2008)=a-ib holds good is