+81 How many positive integers less than 2024 cannot be expressed as the difference of the squares of two positive integers?
What I have deduced so far is that the number cannot be a perfect square, it cannot be an odd number, and it has to be in the form 2 * (some other numbers). The first two has to be only to the power of 1, if it is to the power of two or higher, than it can also be written as two squares. Could anyone help me procced from here? Thanks!
+129845 Not sure about this but notice (NP =not possible)
b^2 - a^2 b^2 a^2
1 1 0 (violates our rules.... a,b must be positive)
2 NP
3 2 1
4 2 0 (violates our rules)
5 3 2
6 NP
7 4 3
8 3 1
9 5 4
10 NP
11 6 5
12 4 2
13 7 6
14 NP
15 8 7
16 5 3
17 9 8
18 NP
It appears that all odds (except 1) can be made
And it appears that all evens can be made except 4 and the ones of the form 2 + 4(n -1) where n = 1,2,3,4....
You should check for yourself with a few values !!!
Note that when n = 506 2 + 4 (506 - 1) = 2022
So.....the answer should be 2 values = (1,4) + 506 values = 508 integers cannot be made
Hope that helps....
