Can you find a general formula

Question

Benjamin likes numbers that can be written as the difference between two perfect squares. He thinks they’re hip. For example, the number 40 is hip, since it equals 7²−3², or 49−9. But hold the phone, 40 is doubly hip, because it also equals 11²−9², or 121−81.

Now, Benjamin is upping the stakes. He wants to know just how hip 1,400 might be. Can you do him a favor, and figure out how many ways 1,400 can be written as the difference of two perfect squares? Benjamin will really appreciate it.

Can you find a general formula or approach for counting the number of ways anywhole number can be written as the difference between two perfect squares? (Your approach might be a function of whether the number is even or odd, its prime factorization, etc.)

Answer 1

x² - y² = 40, (x + y)(x - y) = 1400 = 70·20 = 140·10 = 700·2 ....

x + y = 70 x + y = 140

x - y = 20 x - y = 10

x = 45, y = 25 x = 75, y = 65

45² - 25² =1400 75² - 65² = 1400 ....l

General formula DNE, you have to use any possible factoring of number by 2 factors( both even or both odd)