What is the greatest positive integer n for which n3 + 244 is divisible by n + 8?

• We can apply the remainder theorem, which is when f(x) is divided by (x-a) the remainder will be f(a)
  
  So, when n ^ 3 is divided by n+8, which is (n-(-8), the remainder will be
  (-8) ^ 3 + 244 = -268
  
  So, the remainder is -268, if the number is 268 or a factor of it, the entire expression is divisible .
  
  So, the possible valus of (n+8) are 268, 134,67, 4, 2 , 1
  So, the possible values of n are 260, 126, 59
  
  So, the maximum possible value of n is 260
  
  Answer is 260
• 11 years agoHelpfull: Yes(16) No(0)
• try to make it in form of (n+8) i.e add and substract 8^3=512 on the given eqation n3+244+512-512=n3+8^3-268=(n+8)(n2+8n+64)-268 so so only 268 can completely divide
  268
  so n+8=268 =>n=260
• 11 years agoHelpfull: Yes(5) No(0)