Full text: The collected mathematical papers of Arthur Cayley, Sc.D., F.R.S., late sadlerian professor of pure mathematics in the University of Cambridge (Vol. 10)

696] 
CALCULATION OP THE MINIMUM N.G.F. OF THE BINARY SEVENTHIC. 
X* = 
x 7 = 
x> = 
x Q = 
x, n = 
x,= 
°1 
2 3 
4 5 
6- 
! 
8 9 
lOn 
12 13 
14 
1 
1 
3 
5 
9 
13 
- 
24 
- 
36 
- 
47 
— 
66 
- 
84 
- 
113 
- 
141 
183 
110 
136 
163 
199 
235 
282 
331 
391 
- 
86 
- 
96 
- 
115 
- 
127 
- 
149 
- 
166 
- 
191 
- 
212 
0 
+ 
4 
4* 
2 
+ 
7 
+ 
5 
+ 
8 
+ 
8 
+ 
9 
1 
1 
3 
5 
9 
13 
- 
47 
- 
66 
- 
84 
- 
113 
- 
141 
- 
183 
- 
225 
199 
235 
282 
331 
391 
454 
532 
- 
149 
- 
166 
- 
192 
- 
212 
- 
245 
- 
269 
- 
307 
3 
+ 
4 
+ 
7 
+ 
9 
+ 
10 
+ 
11 
+ 
13 
1 
1 
3 
5 
9 
13 
22 
- 
66 
- 
84 
- 
113 
- 
141 
- 
183 
- 
225 
- 
284 
— 
344 
282 
331 
391 
454 
532 
612 
709 
811 
- 
212 
- 
245 
- 
269 
- 
307 
- 
338 
- 
382 
- 
419 
- 
472 
4 
+ 
3 
10 
+ 
9 
+ 
16 
14 
+ 
19 
17 
1 
1 
3 
5 
9 
13 
22 
— 
113 
— 
141 
- 
183 
— 
225 
— 
284 
— 
344 
— 
425 
454 
532 
612 
709 
811 
931 
1057 
- 
338 
- 
382 
- 
419 
- 
472 
- 
515 
- 
576 
- 
629 
4 
+ 
10 
+ 
13 
+ 
17 
+ 
21 
+ 
24 
+ 
25 
1 
1 
3 
5 
9 
13 
22 
30 
— 
141 
— 
183 
— 
225 
— 
284 
344 
- 
425 
- 
508 
- 
617 
612 
709 
811 
931 
1057 
1206 
1360 
1540 
- 
472 
- 
515 
- 
576 
- 
629 
- 
699 
- 
760 
- 
843 
- 
913 
0 
+ 
12 
+ 
13 
+ 
23 
+ 
23 
+ 
34 
+ 
31 
+ 
40 
1 
3 
5 
9 
13 
22 
30 
— 
225 
— 
284 
— 
344 
- 
425 
— 
508 
- 
617 
- 
729 
931 
1057 
1206 
1360 
1540 
1729 
1945 
- 
699 
- 
760 
- 
843 
- 
913 
- 
1007 
- 
1091 
- 
1197 
8 
+ 
16 
+ 
24 
+ 
31 
+ 
38 
+ 
43 
+ 
49 
1 
3 
5 
9 
13 
22 
30 
45 
— 
284 
— 
344 
— 
425 
- 
508 
- 
617 
— 
729 
- 
872 
- 
1020 
1206 
1360 
1540 
1729 
1945 
2172 
2432 
2702 
- 
913 
- 
1007 
- 
1091 
- 
1197 
- 
1293 
- 
1416 
- 
1525 
- 
1663 
10 
+ 
12 
+ 
29 
+ 
33 
+ 
48 
+ 
49 
+ 
65 
+ 
64 
53 
417
	        
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