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|
Brahmagupta-Fibonacci |
|
|
|
Nombres qui peuvent s'exprimer sous la forme de -
le produit de la somme de deux
carrés -
la somme de deux carrés, de deux
façons (identiques ou différentes) -
la somme de quatre carrés |
Exemple de lecture dans la table 25
=
(2² + 1²) (2² + 1²) = 5² + 0² = 3² + 4² = 4² + 2² + 2² + 1² |
|
|
Toutes
les valeurs de N par ordre croissant et pour (a, b, c, d) = {1, 2, … , 9} |
||
Voir Identité de Brahmagupta-Fibonacci
|
N |
N = (a² + b²) (c² + d²) |
N = E² + F² |
N = E'² + F'² |
N = u² + v² + w² + t² |
||||||||
|
a |
b |
c |
d |
E |
F |
E' |
F' |
u |
v |
w |
t |
|
|
ac+bd |
ad-bc |
ac-bd |
ad+bc |
ac |
ad |
bc |
bd |
|||||
|
4 |
1 |
1 |
1 |
1 |
2 |
0 |
0 |
2 |
1 |
1 |
1 |
1 |
|
10 |
2 |
1 |
1 |
1 |
3 |
1 |
1 |
3 |
2 |
2 |
1 |
1 |
|
16 |
2 |
2 |
1 |
1 |
4 |
0 |
0 |
4 |
2 |
2 |
2 |
2 |
|
20 |
3 |
1 |
1 |
1 |
4 |
2 |
2 |
4 |
3 |
3 |
1 |
1 |
|
25 |
2 |
1 |
2 |
1 |
5 |
0 |
3 |
4 |
4 |
2 |
2 |
1 |
|
26 |
3 |
2 |
1 |
1 |
5 |
1 |
1 |
5 |
3 |
3 |
2 |
2 |
|
34 |
4 |
1 |
1 |
1 |
5 |
3 |
3 |
5 |
4 |
4 |
1 |
1 |
|
36 |
3 |
3 |
1 |
1 |
6 |
0 |
0 |
6 |
3 |
3 |
3 |
3 |
|
40 |
4 |
2 |
1 |
1 |
6 |
2 |
2 |
6 |
4 |
4 |
2 |
2 |
|
2 |
2 |
2 |
1 |
6 |
2 |
2 |
6 |
4 |
2 |
4 |
2 |
|
|
50 |
4 |
3 |
1 |
1 |
7 |
1 |
1 |
7 |
4 |
4 |
3 |
3 |
|
3 |
1 |
2 |
1 |
7 |
1 |
5 |
5 |
6 |
3 |
2 |
1 |
|
|
52 |
5 |
1 |
1 |
1 |
6 |
4 |
4 |
6 |
5 |
5 |
1 |
1 |
|
58 |
5 |
2 |
1 |
1 |
7 |
3 |
3 |
7 |
5 |
5 |
2 |
2 |
|
64 |
4 |
4 |
1 |
1 |
8 |
0 |
0 |
8 |
4 |
4 |
4 |
4 |
|
2 |
2 |
2 |
2 |
8 |
0 |
0 |
8 |
4 |
4 |
4 |
4 |
|
|
65 |
3 |
2 |
2 |
1 |
8 |
1 |
4 |
7 |
6 |
3 |
4 |
2 |
|
68 |
5 |
3 |
1 |
1 |
8 |
2 |
2 |
8 |
5 |
5 |
3 |
3 |
|
74 |
6 |
1 |
1 |
1 |
7 |
5 |
5 |
7 |
6 |
6 |
1 |
1 |
|
80 |
6 |
2 |
1 |
1 |
8 |
4 |
4 |
8 |
6 |
6 |
2 |
2 |
|
2 |
2 |
3 |
1 |
8 |
4 |
4 |
8 |
6 |
2 |
6 |
2 |
|
|
82 |
5 |
4 |
1 |
1 |
9 |
1 |
1 |
9 |
5 |
5 |
4 |
4 |
|
85 |
4 |
1 |
2 |
1 |
9 |
2 |
7 |
6 |
8 |
4 |
2 |
1 |
|
90 |
6 |
3 |
1 |
1 |
9 |
3 |
3 |
9 |
6 |
6 |
3 |
3 |
|
3 |
3 |
2 |
1 |
9 |
3 |
3 |
9 |
6 |
3 |
6 |
3 |
Pour retrouver les propriétés de tous ces
nombres voir Diconombre
|
100 |
7 |
1 |
1 |
1 |
8 |
6 |
6 |
8 |
7 |
7 |
1 |
1 |
|
5 |
5 |
1 |
1 |
10 |
0 |
0 |
10 |
5 |
5 |
5 |
5 |
|
|
4 |
2 |
2 |
1 |
10 |
0 |
6 |
8 |
8 |
4 |
4 |
2 |
|
|
3 |
1 |
3 |
1 |
10 |
0 |
8 |
6 |
9 |
3 |
3 |
1 |
|
|
104 |
6 |
4 |
1 |
1 |
10 |
2 |
2 |
10 |
6 |
6 |
4 |
4 |
|
3 |
2 |
2 |
2 |
10 |
2 |
2 |
10 |
6 |
6 |
4 |
4 |
|
|
106 |
7 |
2 |
1 |
1 |
9 |
5 |
5 |
9 |
7 |
7 |
2 |
2 |
|
116 |
7 |
3 |
1 |
1 |
10 |
4 |
4 |
10 |
7 |
7 |
3 |
3 |
|
122 |
6 |
5 |
1 |
1 |
11 |
1 |
1 |
11 |
6 |
6 |
5 |
5 |
|
125 |
4 |
3 |
2 |
1 |
11 |
2 |
5 |
10 |
8 |
4 |
6 |
3 |
|
130 |
8 |
1 |
1 |
1 |
9 |
7 |
7 |
9 |
8 |
8 |
1 |
1 |
|
7 |
4 |
1 |
1 |
11 |
3 |
3 |
11 |
7 |
7 |
4 |
4 |
|
|
5 |
1 |
2 |
1 |
11 |
3 |
9 |
7 |
10 |
5 |
2 |
1 |
|
|
3 |
2 |
3 |
1 |
11 |
3 |
7 |
9 |
9 |
3 |
6 |
2 |
|
|
136 |
8 |
2 |
1 |
1 |
10 |
6 |
6 |
10 |
8 |
8 |
2 |
2 |
|
2 |
2 |
4 |
1 |
10 |
6 |
6 |
10 |
8 |
2 |
8 |
2 |
|
|
144 |
6 |
6 |
1 |
1 |
12 |
0 |
0 |
12 |
6 |
6 |
6 |
6 |
|
145 |
5 |
2 |
2 |
1 |
12 |
1 |
8 |
9 |
10 |
5 |
4 |
2 |
|
146 |
8 |
3 |
1 |
1 |
11 |
5 |
5 |
11 |
8 |
8 |
3 |
3 |
|
148 |
7 |
5 |
1 |
1 |
12 |
2 |
2 |
12 |
7 |
7 |
5 |
5 |
|
160 |
8 |
4 |
1 |
1 |
12 |
4 |
4 |
12 |
8 |
8 |
4 |
4 |
|
4 |
4 |
2 |
1 |
12 |
4 |
4 |
12 |
8 |
4 |
8 |
4 |
|
|
4 |
2 |
2 |
2 |
12 |
4 |
4 |
12 |
8 |
8 |
4 |
4 |
|
|
164 |
9 |
1 |
1 |
1 |
10 |
8 |
8 |
10 |
9 |
9 |
1 |
1 |
|
169 |
3 |
2 |
3 |
2 |
13 |
0 |
5 |
12 |
9 |
6 |
6 |
4 |
|
170 |
9 |
2 |
1 |
1 |
11 |
7 |
7 |
11 |
9 |
9 |
2 |
2 |
|
7 |
6 |
1 |
1 |
13 |
1 |
1 |
13 |
7 |
7 |
6 |
6 |
|
|
5 |
3 |
2 |
1 |
13 |
1 |
7 |
11 |
10 |
5 |
6 |
3 |
|
|
4 |
1 |
3 |
1 |
13 |
1 |
11 |
7 |
12 |
4 |
3 |
1 |
|
|
178 |
8 |
5 |
1 |
1 |
13 |
3 |
3 |
13 |
8 |
8 |
5 |
5 |
|
180 |
9 |
3 |
1 |
1 |
12 |
6 |
6 |
12 |
9 |
9 |
3 |
3 |
|
3 |
3 |
3 |
1 |
12 |
6 |
6 |
12 |
9 |
3 |
9 |
3 |
|
|
185 |
6 |
1 |
2 |
1 |
13 |
4 |
11 |
8 |
12 |
6 |
2 |
1 |
|
194 |
9 |
4 |
1 |
1 |
13 |
5 |
5 |
13 |
9 |
9 |
4 |
4 |
|
196 |
7 |
7 |
1 |
1 |
14 |
0 |
0 |
14 |
7 |
7 |
7 |
7 |
|
200 |
8 |
6 |
1 |
1 |
14 |
2 |
2 |
14 |
8 |
8 |
6 |
6 |
|
6 |
2 |
2 |
1 |
14 |
2 |
10 |
10 |
12 |
6 |
4 |
2 |
|
|
4 |
2 |
3 |
1 |
14 |
2 |
10 |
10 |
12 |
4 |
6 |
2 |
|
|
4 |
3 |
2 |
2 |
14 |
2 |
2 |
14 |
8 |
8 |
6 |
6 |
|
|
205 |
5 |
4 |
2 |
1 |
14 |
3 |
6 |
13 |
10 |
5 |
8 |
4 |
|
208 |
2 |
2 |
5 |
1 |
12 |
8 |
8 |
12 |
10 |
2 |
10 |
2 |
|
212 |
9 |
5 |
1 |
1 |
14 |
4 |
4 |
14 |
9 |
9 |
5 |
5 |
|
221 |
3 |
2 |
4 |
1 |
14 |
5 |
10 |
11 |
12 |
3 |
8 |
2 |
|
225 |
6 |
3 |
2 |
1 |
15 |
0 |
9 |
12 |
12 |
6 |
6 |
3 |
|
226 |
8 |
7 |
1 |
1 |
15 |
1 |
1 |
15 |
8 |
8 |
7 |
7 |
|
232 |
5 |
2 |
2 |
2 |
14 |
6 |
6 |
14 |
10 |
10 |
4 |
4 |
|
234 |
9 |
6 |
1 |
1 |
15 |
3 |
3 |
15 |
9 |
9 |
6 |
6 |
|
3 |
3 |
3 |
2 |
15 |
3 |
3 |
15 |
9 |
6 |
9 |
6 |
|
|
250 |
7 |
1 |
2 |
1 |
15 |
5 |
13 |
9 |
14 |
7 |
2 |
1 |
|
5 |
5 |
2 |
1 |
15 |
5 |
5 |
15 |
10 |
5 |
10 |
5 |
|
|
4 |
3 |
3 |
1 |
15 |
5 |
9 |
13 |
12 |
4 |
9 |
3 |
|
|
256 |
8 |
8 |
1 |
1 |
16 |
0 |
0 |
16 |
8 |
8 |
8 |
8 |
|
260 |
9 |
7 |
1 |
1 |
16 |
2 |
2 |
16 |
9 |
9 |
7 |
7 |
|
6 |
4 |
2 |
1 |
16 |
2 |
8 |
14 |
12 |
6 |
8 |
4 |
|
|
5 |
1 |
3 |
1 |
16 |
2 |
14 |
8 |
15 |
5 |
3 |
1 |
|
|
4 |
2 |
3 |
2 |
16 |
2 |
8 |
14 |
12 |
8 |
6 |
4 |
|
|
265 |
7 |
2 |
2 |
1 |
16 |
3 |
12 |
11 |
14 |
7 |
4 |
2 |
|
272 |
5 |
3 |
2 |
2 |
16 |
4 |
4 |
16 |
10 |
10 |
6 |
6 |
|
289 |
4 |
1 |
4 |
1 |
17 |
0 |
15 |
8 |
16 |
4 |
4 |
1 |
|
290 |
9 |
8 |
1 |
1 |
17 |
1 |
1 |
17 |
9 |
9 |
8 |
8 |
|
7 |
3 |
2 |
1 |
17 |
1 |
11 |
13 |
14 |
7 |
6 |
3 |
|
|
5 |
2 |
3 |
1 |
17 |
1 |
13 |
11 |
15 |
5 |
6 |
2 |
|
|
296 |
2 |
2 |
6 |
1 |
14 |
10 |
10 |
14 |
12 |
2 |
12 |
2 |
|
305 |
6 |
5 |
2 |
1 |
17 |
4 |
7 |
16 |
12 |
6 |
10 |
5 |
|
306 |
3 |
3 |
4 |
1 |
15 |
9 |
9 |
15 |
12 |
3 |
12 |
3 |
|
320 |
4 |
4 |
3 |
1 |
16 |
8 |
8 |
16 |
12 |
4 |
12 |
4 |
|
6 |
2 |
2 |
2 |
16 |
8 |
8 |
16 |
12 |
12 |
4 |
4 |
|
|
324 |
9 |
9 |
1 |
1 |
18 |
0 |
0 |
18 |
9 |
9 |
9 |
9 |
|
3 |
3 |
3 |
3 |
18 |
0 |
0 |
18 |
9 |
9 |
9 |
9 |
|
|
325 |
8 |
1 |
2 |
1 |
17 |
6 |
15 |
10 |
16 |
8 |
2 |
1 |
|
7 |
4 |
2 |
1 |
18 |
1 |
10 |
15 |
14 |
7 |
8 |
4 |
|
|
4 |
3 |
3 |
2 |
18 |
1 |
6 |
17 |
12 |
8 |
9 |
6 |
|
|
328 |
5 |
4 |
2 |
2 |
18 |
2 |
2 |
18 |
10 |
10 |
8 |
8 |
|
338 |
3 |
2 |
5 |
1 |
17 |
7 |
13 |
13 |
15 |
3 |
10 |
2 |
|
340 |
8 |
2 |
2 |
1 |
18 |
4 |
14 |
12 |
16 |
8 |
4 |
2 |
|
5 |
3 |
3 |
1 |
18 |
4 |
12 |
14 |
15 |
5 |
9 |
3 |
|
|
4 |
2 |
4 |
1 |
18 |
4 |
14 |
12 |
16 |
4 |
8 |
2 |
|
|
360 |
6 |
6 |
2 |
1 |
18 |
6 |
6 |
18 |
12 |
6 |
12 |
6 |
|
6 |
3 |
2 |
2 |
18 |
6 |
6 |
18 |
12 |
12 |
6 |
6 |
|
|
3 |
3 |
4 |
2 |
18 |
6 |
6 |
18 |
12 |
6 |
12 |
6 |
|
|
365 |
8 |
3 |
2 |
1 |
19 |
2 |
13 |
14 |
16 |
8 |
6 |
3 |
|
370 |
7 |
5 |
2 |
1 |
19 |
3 |
9 |
17 |
14 |
7 |
10 |
5 |
|
6 |
1 |
3 |
1 |
19 |
3 |
17 |
9 |
18 |
6 |
3 |
1 |
|
|
377 |
5 |
2 |
3 |
2 |
19 |
4 |
11 |
16 |
15 |
10 |
6 |
4 |
|
400 |
8 |
4 |
2 |
1 |
20 |
0 |
12 |
16 |
16 |
8 |
8 |
4 |
|
6 |
2 |
3 |
1 |
20 |
0 |
16 |
12 |
18 |
6 |
6 |
2 |
|
|
2 |
2 |
7 |
1 |
16 |
12 |
12 |
16 |
14 |
2 |
14 |
2 |
|
|
5 |
5 |
2 |
2 |
20 |
0 |
0 |
20 |
10 |
10 |
10 |
10 |
|
|
4 |
2 |
4 |
2 |
20 |
0 |
12 |
16 |
16 |
8 |
8 |
4 |
|
|
410 |
9 |
1 |
2 |
1 |
19 |
7 |
17 |
11 |
18 |
9 |
2 |
1 |
|
5 |
4 |
3 |
1 |
19 |
7 |
11 |
17 |
15 |
5 |
12 |
4 |
|
|
416 |
6 |
4 |
2 |
2 |
20 |
4 |
4 |
20 |
12 |
12 |
8 |
8 |
|
4 |
4 |
3 |
2 |
20 |
4 |
4 |
20 |
12 |
8 |
12 |
8 |
|
|
424 |
7 |
2 |
2 |
2 |
18 |
10 |
10 |
18 |
14 |
14 |
4 |
4 |
|
425 |
9 |
2 |
2 |
1 |
20 |
5 |
16 |
13 |
18 |
9 |
4 |
2 |
|
7 |
6 |
2 |
1 |
20 |
5 |
8 |
19 |
14 |
7 |
12 |
6 |
|
|
4 |
3 |
4 |
1 |
19 |
8 |
13 |
16 |
16 |
4 |
12 |
3 |
|
|
442 |
5 |
1 |
4 |
1 |
21 |
1 |
19 |
9 |
20 |
5 |
4 |
1 |
|
5 |
3 |
3 |
2 |
21 |
1 |
9 |
19 |
15 |
10 |
9 |
6 |
|
|
445 |
8 |
5 |
2 |
1 |
21 |
2 |
11 |
18 |
16 |
8 |
10 |
5 |
|
450 |
9 |
3 |
2 |
1 |
21 |
3 |
15 |
15 |
18 |
9 |
6 |
3 |
|
6 |
3 |
3 |
1 |
21 |
3 |
15 |
15 |
18 |
6 |
9 |
3 |
|
|
4 |
3 |
3 |
3 |
21 |
3 |
3 |
21 |
12 |
12 |
9 |
9 |
|
|
464 |
7 |
3 |
2 |
2 |
20 |
8 |
8 |
20 |
14 |
14 |
6 |
6 |
|
468 |
3 |
3 |
5 |
1 |
18 |
12 |
12 |
18 |
15 |
3 |
15 |
3 |
|
481 |
3 |
2 |
6 |
1 |
20 |
9 |
16 |
15 |
18 |
3 |
12 |
2 |
|
485 |
9 |
4 |
2 |
1 |
22 |
1 |
14 |
17 |
18 |
9 |
8 |
4 |
|
488 |
6 |
5 |
2 |
2 |
22 |
2 |
2 |
22 |
12 |
12 |
10 |
10 |
|
490 |
7 |
7 |
2 |
1 |
21 |
7 |
7 |
21 |
14 |
7 |
14 |
7 |
|
493 |
5 |
2 |
4 |
1 |
22 |
3 |
18 |
13 |
20 |
5 |
8 |
2 |
|
500 |
8 |
6 |
2 |
1 |
22 |
4 |
10 |
20 |
16 |
8 |
12 |
6 |
|
7 |
1 |
3 |
1 |
22 |
4 |
20 |
10 |
21 |
7 |
3 |
1 |
|
|
5 |
5 |
3 |
1 |
20 |
10 |
10 |
20 |
15 |
5 |
15 |
5 |
|
|
4 |
3 |
4 |
2 |
22 |
4 |
10 |
20 |
16 |
8 |
12 |
6 |
|
Suite |
|
|
Voir |
