Latest TCS Aptitude Question SOLUTION: What is the greatest positive integer n for which n3 + 244 is divisible by n + 8?

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

Asked In TCS `yannam jyothi reddy (11 years ago)

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Mahesh  (11 years ago)

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

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krittika  (11 years ago)

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

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