Question

What is the largest integer n such that (n^2-38) / (n +1) is an integer?

a. 36
b. 38
c. 72
d. 76
e. None of these

Answer 1

a. 36

Explanation:

for (n^2-38)/(n+1) to be an integer, n+1 must completely divide, n^2-38.

we check with the options

option a n=36 sutisfies the above condition.

(36^2-38)/36+1 = 1258/37= 34 , which is an integer. Therefore, largest integer would be 36