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tc balıkesir üniversitesi fen bilimleri enstitüsü matematik anabilim ...

tc balıkesir üniversitesi fen bilimleri enstitüsü matematik anabilim ...

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2 3 2<br />

EK C : “ y = x − 1 x(mod 17)<br />

EĞRİSİ ÜZERİNDEKİ NOKTALAR, BU<br />

NOKTALARIN KUVVETLERİ VE MERTEBELERİ”<br />

x y MOD n MERT. KUV. x y x y x y x y x y x y x y x y x y x y x y x y x y x y x y<br />

0 0 17 -1 2 1 0 0 1 0 4 3 4 14 5 1 5 16 7 8 7 9 10 2 10 15 12 4 12 13 13 5 13 12 16 0<br />

1 0 17 -1 2 2 0 0 0 0 16 0 16 0 1 0 1 0 16 0 16 0 1 0 1 0 0 0 0 0<br />

4 3 17 -1 4 3 4 14 4 3 5 16 5 1 7 9 7 8 10 15 10 2 12 13 12 4 13 12 13 5<br />

4 14 17 -1 4<br />

5 1 17 -1 4<br />

5 16 17 -1 4<br />

7 8 17 -1 4<br />

7 9 17 -1 4<br />

10 2 17 -1 4<br />

10 15 17 -1 4<br />

12 4 17 -1 4<br />

12 13 17 -1 4<br />

13 5 17 -1 4<br />

13 12 17 -1 4<br />

16 0 17 -1 2<br />

E 17<br />

16<br />

15<br />

14<br />

13<br />

12<br />

11<br />

10<br />

9<br />

8<br />

7<br />

6<br />

5<br />

4<br />

3<br />

2<br />

1<br />

4, 14<br />

4, 3<br />

5, 16<br />

5, 1<br />

x^3 - x (mod 17)<br />

7, 9<br />

7, 8<br />

0 0, 0, 0<br />

0<br />

1, 0<br />

16, 16, 16, 0 0<br />

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16<br />

E17 81<br />

10, 15<br />

10, 2<br />

12, 13<br />

12, 4<br />

13, 12<br />

13, 5

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