| Sums of the n-th Powers of Zeros |
| 1 |
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| |
3 |
|
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| |
0 |
|
|
|
|
|
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| |
2 |
0 |
0 |
0 |
0 |
0 |
0 |
| |
0 |
-3 |
0 |
0 |
0 |
0 |
0 |
| |
2 |
0 |
0 |
0 |
0 |
0 |
0 |
| |
0 |
-5 |
0 |
0 |
0 |
0 |
0 |
| |
2 |
0 |
3 |
0 |
0 |
0 |
0 |
| |
0 |
-7 |
0 |
0 |
0 |
0 |
0 |
| |
2 |
0 |
8 |
0 |
0 |
0 |
0 |
| |
0 |
-9 |
0 |
-3 |
0 |
0 |
0 |
| |
2 |
0 |
15 |
0 |
0 |
0 |
0 |
| |
0 |
-11 |
0 |
-11 |
0 |
0 |
0 |
| |
2 |
0 |
24 |
0 |
3 |
0 |
0 |
| |
0 |
-13 |
0 |
-26 |
0 |
0 |
0 |
| |
2 |
0 |
35 |
0 |
14 |
0 |
0 |
| |
0 |
-15 |
0 |
-50 |
0 |
-3 |
0 |
| |
2 |
0 |
48 |
0 |
40 |
0 |
0 |
| |
0 |
-17 |
0 |
-85 |
0 |
-17 |
0 |
| |
2 |
0 |
63 |
0 |
90 |
0 |
3 |
Let a , b
, g be the zeros of the
equation x3 - px + q = 0.
Then the sum w(17) = a17
+ b17 + g17
= - 17p7q - 85p4q3
-17pq5 .
Reference: T.S. Nanjundiah, A note on an identity of Ramanujan,
Amer. Math. Monthly, 100(5), 485-487.