Find the non-zero integral solutions of `|1-i|^x=2^x`.

Find the number of non-zero integral solutions of the equation |1- i|^x= 2^x .

Number of non-zero integral solutions of the equation |1-i|^x= 2^x is :

Find the number of integral solutions of equation x+y+z+t=29, when x >= 1, y >= 2, z>=3 and t >= 0

Find the number of non-negative integral solutions of x_1+x_2+x_3+4x_4=20.

Find the number of positive integral solutions of tan^-1 x + cot^-1 y = tan^-1 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.

Find the integral solutions to the equation [x][y]=x+y . Show that all the non-integral solutions lie on exactly two lines. Determine these lines. Here [.] denotes greatest integer function.

The number of non negative integral solutions of 3x+y+z=24 is

Number of ways in which 15 identical coins can be put into 6 different bags (i) is coefficient of x^(15) in x^(6)(1+x+x^(2)+ . . .oo)^(6), if no bag remains empty (ii) is coefficient of x^(15) in (1-x)^(-6) (iii) is same as number of the integral solutions of (iv)is same as number of non-negative integral solutions of underset(i=1)overset(6)(sum)x_(i)=15