Algebra...A.P. >=G.P.

apgp

greatest integer fn...

if 76 < x< 92 and 142 < x< 2003; then how many solutions are possible for the following equation:
[x/143] + [2x/91] + [3x/77] = 68x/1001
where [x] represents greatest integer less than equal to x.

remainders..

Let p = x²⁵-x¹³+x⁶-1 ; where x>2007.
How many remainders are possible if p is divided by 7???

Functions

*Let f(x) be a function satisfying f(x)f(y)=f(xy) for all real x, y. if f(2)= 4, then what is the value of f(1/2)?
a. 0
b. 1/4
c. 1/2
d. cannot be determined
e. 1