A teacher asked her students to think of a natural no which was a perfect square and convert it to a base pf any natural number not more than 9.She observed that even though no 2 students converted to the same base,all the students ended up getting the same result of 12321.Find the max number of students in the class

1) 4
2) 5
3) 6
4) 7

• 6
  
  (12321) base n= n^4 + 2n^3 + 3n^2 + 2n +1 =(n^2 + n + 1)^2
  
  with any base , 12321 will be a perfect square.
  but n can not be more than 9 and also n=1,2,3 not possible as these numbers are used.
  
  so max possible number of students is 6.
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