Ramesh asked each of his friends to think of a natural number which is a perfect square and then convert it to a number system to the base of any natural number of their choice, where the base is not more than 9. Ramesh later observed that though no two of his friends took the same base all the friends ended up with the same result 12321. Find maximum possible number of friends whom Ramesh asked the question.

1) 3
2) 8
3) 7
4) 6

• 12321 in base n = n^4+2n^3+3n^2+2n+1 = (n^2+n+1)^2 which is always a perfect square.
  
  so any base from 4 to 9 will satisfy the condition.
  
  so max 6 friends.
• 11 years agoHelpfull: Yes(0) No(0)