Determine all possible value(s) of a 4-digit non leading zero base ten positive integer x such that the remainder obtained upon dividing 2^x by 10,000 is equal to x.

What are the possible value(s) of a 4-digit non leading zero base ten positive integer x such that the remainder obtained upon dividing 3^x by 10,000 is equal to x?

actually its fairly simple to implement in Qbasic as well

cls 0
b=2
pwrb=1
for x=1 to 999
 pwrb=(pwrb*b) mod 10000
next x
for x=1000 to 9999
 pwrb=(pwrb*b) mod 10000
 if pwrb=x then
  print x
 end if
next x

quickly finds 8736 for 2^x and changing b=2 to b=3 finds 5387 for 3^x

Posted by Daniel on 2009-08-20 11:24:10