There are exactly two(2) positive integers such that (n + 1)^3 / (n + 20) is an integer. What are the 2 integers?. Thank you for help.
+129849 ( n + 1)^3
_______ simplifies to n^2 - 17n - 6869 + 343
n + 20 _____
n + 20
6859 factors as 19^3
So....19^2 will divide 6859......so
n + 20 = 19^2
n = 19^2 - 20 = 341
Also....19^3 will divide 6859....so
n + 20 = 19^3
n = 19^3 - 20 = 6839
So.....the two positive integers are n = 341 and n = 6839
