abstract algebra help please!

[cuti3panda]

this problem is due on wedd. , i hope you guys will help me out with this....

 

In the cut "As" from Songs in the Key of Life, Stevie Wonder mentions the equation 8 x 8 x 8 x 8 = 4. Find all integers n for which this statement is true, molulo n.

 

thanks alot for your help......

[fuhrerkeebs]

Well, since x mod y = x-y*[x/y] ([] is the integer function), you know that n*[4096/n]=4092. This says that the only valid values are when n<=4092. Knowing this, I used by good ol' Qbasic to get all of the possible values for n. The equation holds only for values of n where n=6,11,12,22,31,33,44,62,66,93,124,132,186,341,372,682,1023,1364,2046, and 4092.