Find number of integers n such that `n^4-n^2+64` is the square of an integer.

Find the number of integers n for which (n)/(20-n) is the square of an integer.

Find the sum of all those integers n for which n^2+20n+15 is the square of an integer.

Find the number of positive integers n such that 105 is a divisor of n^2+n+1.

Find the number of positive integers n such that 105 is a divisor of n^(2)+n+1

Suppose n is a positive integer such that (n^2 + 48) is a perfect square. What is the number of such n? (n<5)

Let m be the smallest odd positive iteger for which 1 + 2+ …..+ m is a square of an integer and let n be the smallest even positive integer for which 1 + 2+ ……+ n is a square of an integer. What is the value of m + n ?