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Squares mod primes
| n |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
25
|
| n2
|
1
|
4
|
9
|
16
|
25
|
36
|
49
|
64
|
81
|
100 |
121 |
144 |
169 |
196 |
225 |
256 |
289 |
324 |
361 |
400 |
441 |
484 |
529 |
576 |
625
|
| mod 3
|
1 |
1 |
0
|
1 |
1 |
0
|
1 |
1 |
0
|
1 |
1 |
0
|
1 |
1 |
0
|
1 |
1 |
0
|
1 |
1 |
0
|
1 |
1 |
0
|
1
|
| mod 5
|
1 |
4 |
4 |
1 |
0
|
1 |
4 |
4 |
1 |
0
|
1 |
4 |
4 |
1 |
0
|
1 |
4 |
4 |
1 |
0
|
1 |
4 |
4 |
1 |
0
|
| mod 7
|
1 |
4 |
2 |
2 |
4 |
1 |
0
|
1 |
4 |
2 |
2 |
4 |
1 |
0
|
1 |
4 |
2 |
2 |
4 |
1 |
0
|
1 |
4 |
2 |
2
|
| mod 11
|
1 |
4 |
9 |
5 |
3 |
3 |
5 |
9 |
4 |
1 |
0
|
1 |
4 |
9 |
5 |
3 |
3 |
5 |
9 |
4 |
1 |
0
|
1 |
4 |
9
|
| mod 13
|
1 |
4 |
9 |
3 |
12 |
10 |
10 |
12 |
3 |
9 |
4 |
1 |
0
|
1 |
4 |
9 |
3 |
12 |
10 |
10 |
12 |
3 |
9 |
4 |
1
|
| mod 17
|
1 |
4 |
9 |
16 |
8 |
2 |
15 |
13 |
13 |
15 |
2 |
8 |
16 |
9 |
4 |
1 |
0
|
1 |
4 |
9 |
16 |
8 |
2 |
15 |
13
|
| mod 19
|
1 |
4 |
9 |
16 |
6 |
17 |
11 |
7 |
5 |
5 |
7 |
11 |
17 |
6 |
16 |
9 |
4 |
1 |
0
|
1 |
4 |
9 |
16 |
6 |
17
|
| mod 23
|
1 |
4 |
9 |
16 |
2 |
13 |
3 |
18 |
12 |
8 |
6 |
6 |
8 |
12 |
18 |
3 |
13 |
2 |
16 |
9 |
4 |
1 |
0
|
1 |
4
|
| mod 29
|
1 |
4 |
9 |
16 |
25 |
7 |
20 |
6 |
23 |
13 |
5 |
28 |
24 |
22 |
22 |
24 |
28 |
5 |
13 |
23 |
6 |
20 |
7 |
25 |
16
|
| mod 31
|
1 |
4 |
9 |
16 |
25 |
5 |
18 |
2 |
19 |
7 |
28 |
20 |
14 |
10 |
8 |
8 |
10 |
14 |
20 |
28 |
7 |
19 |
2 |
18 |
5
|
| mod 37
|
1 |
4 |
9 |
16 |
25 |
36 |
12 |
27 |
7 |
26 |
20 |
33 |
21 |
11 |
3 |
34 |
30 |
28 |
28 |
30 |
34 |
3 |
11 |
21 |
33
|
| mod 41
|
1 |
4 |
9 |
16 |
25 |
36 |
8 |
23 |
40 |
18 |
39 |
21 |
5 |
32 |
20 |
10 |
2 |
37 |
33 |
31 |
31 |
33 |
37 |
2 |
10
|
| mod 43
|
1 |
4 |
9 |
16 |
25 |
36 |
6 |
21 |
38 |
14 |
35 |
15 |
40 |
24 |
10 |
41 |
31 |
23 |
17 |
13 |
11 |
11 |
13 |
17 |
23
|
| mod 47
|
1 |
4 |
9 |
16 |
25 |
36 |
2 |
17 |
34 |
6 |
27 |
3 |
28 |
8 |
37 |
21 |
7 |
42 |
32 |
24 |
18 |
14 |
12 |
12 |
14
|
