Squares
I'm looking into Mersenne Primes and always run across problems involving squares. So here are some of the things I need to remember so I put them here for everyone's use.
Here are some interesting power of 2 forms.
All Squares have the following three forms:
| 8k where k = 2n2 n=0 to infinity |
| n |
k=2n2 |
8k |
| 0 |
0 |
0 |
| 1 |
2 |
16 |
| 2 |
8 |
64 |
| 3 |
18 |
144 |
| 8k+1 where k = (n2+n)/2 n=0 to infinity |
| n |
k=(n2+n)/2 |
8k+1 |
| 0 |
0 |
1 |
| 1 |
1 |
9 |
| 2 |
3 |
25 |
| 3 |
6 |
49 |
| 8k+4 where k = 4[ (n2+n)/2] n=0 to infinity |
| n |
k=4[ (n2+n)/2] |
8k+4 |
| 0 |
0 |
4 |
| 1 |
4 |
36 |
| 2 |
12 |
100 |
| 3 |
24 |
196 |