Matematika-informatika” ta`lim yo’nalishi 3-”A” guruh talabasi Karshiyeva Gulnozaning

10.17. 10.25.

Bеrilgan taqqoslamalarni soddalashtiring:

x²³³ + 345x¹³² - 567x¹⁰⁹+ 346x⁹⁸ + 45x⁵⁶ - 463x³⁷ - 24x¹⁵+ x⁹ +467  0 (mod 5);

245x²⁷⁴ + 345x¹²³ - 507x¹¹⁹ + 346x⁹⁸ + 45x⁵⁴ - 463x²⁷ - 24x¹⁵+x - 67  0 (mod 7);

x²³³ + 345x¹³² - 567x¹⁰⁹ + 346x⁹⁸ + 45x⁵⁶ - 463x³⁷ - 24x¹⁵ +x⁹+467  0 (mod 13);

245x²⁷⁴ + 345x¹²³ - 507x¹¹⁹ + 346x⁹⁸ + 45x⁵⁴ - 463x²⁷ -24x¹⁵ -x + 67  0 (mod 11);

5⁴³⁵ + 325x²⁰³ - 57x¹⁰⁰ + 634x⁹⁸ + 45x⁵² - 63x²⁵ - 24x¹⁵+x + 167  0 (mod 3);

45x²⁹⁴ + 545x²²³ - 677x⁹⁷+334x⁹⁰-465x⁵⁷+43x²⁸ -264x¹¹+244x+674  0 (mod 3);

245x²⁷⁴+345x¹²³-507x¹¹⁹+346x⁹⁸ +45x⁵⁴ - 463x²⁷ - 24x¹⁵ +x+67  0 (mod 5);

245x²⁷⁴ + 345x¹²³ + 507x¹¹⁹ + 346x⁹⁸+45x⁵⁴-463x²⁷-24x¹⁵+x+67  0 (mod 13);

x²³³ + 345x¹³² - 567x¹⁰⁹ + 346x⁹⁸+45x⁵⁶-463x³⁷+24x¹⁵ +x⁹+467  0 (mod 3);

x²³³ + 345x¹³² - 567x¹⁰⁹ + 346x⁹⁸ - 45x⁵⁶ -463x³⁷- 24x¹⁵+x⁹+467  0 (mod 11);

x²³³ + 345x¹³² - 567x¹⁰⁹ - 346x⁹⁸ + 45x⁵⁶-463x³⁷ -24x¹⁵+x⁹+467  0 (mod 7);

x²³³ + 345x¹³² - 567x¹⁰⁹ + 346x⁹⁸ + 45x⁵⁶ - 463x³⁷-24x¹⁵+x⁹+467  0 (mod 13);

745x³⁹⁴+545x²²³ - 677x⁹⁷+334x⁹⁰ - 465x⁵⁷-43x²⁸-264x¹¹+244x-674  0 (mod 13);

-45x²⁹⁴ + 545x²²³ - 677x⁹⁷+334x⁹⁰+465x⁵⁷-43x²⁸-264x¹¹-244x+674  0 (mod 5);

453⁵⁹⁴ - 545x²²³ - 677x⁹⁷ + 334x⁹⁰ + 465x⁵⁷ - 43x²⁸-264x¹¹-244x -674  0 (mod 7);

-45x²⁹⁴+545x²²³+677x⁹⁷+334x⁹⁰+465x⁵⁷-43x²⁸-264x¹¹+244x - 674  0 (mod 11);

145x²⁴⁵ - 55x¹²³ - 77x⁹⁹+34x⁹⁵-165x⁵⁰-473x²³-64x¹²+44x⁹ -124  0 (mod 3);

345x²⁴⁵+55x¹²³+77x⁹⁹+34x⁹⁵+165x⁵⁰-473x²³+64x¹² -44x⁹+124  0 (mod 13);

-145x³⁴⁵+55x¹²³ -77x⁹⁹+34x⁹⁵-165x⁵⁰-473x²³ -64x¹²+44x⁹ -124  0 (mod 5);

245x⁴⁴⁵+55x¹²³-77x⁹⁹+34x⁹⁵+165x⁵⁰-473x²³+64x¹² +44x⁹ +124  0 (mod 7);

145x¹⁴⁵ + 76x¹⁰³ -47x⁹⁰+32x⁶⁵+15x⁵-43x²+6x+24  0 (mod 17);

761x³⁴⁵ + 415x²³³-247x¹⁰⁰+337x⁸⁴+195x⁷⁴-73x²³+64x¹²+44x⁹+194  0 (mod 5);

975x²⁸⁵+735x²¹⁴-767x¹¹⁹+394x¹⁰⁵+465x⁷⁰-173x⁶³+344x⁶²+124x⁹¹  0 (mod 7);

763x⁵³⁴+732x³²³-237x¹²⁹+354x¹²⁵+865x¹¹⁰-473x⁹³+604x⁷²+234x¹¹  0 (mod 5);

934x³³³+143x²⁰³-232x¹¹⁹+549x⁹⁴+765x⁵³-73x²⁶+984x²²+49x¹¹ + 9  0 (mod 3).

Lеjandr simvolini aniqlang:

; 12.8. ; 12.14. ; 12.20. ;

; 12.9. ; 12.15. ; 12.21. ;

; 12.10. ; 12.16. ; 12.22. ;

; 12.11. ; 12.17. ; 12.23. ;

; 12.12. ; 12.18. ; 12.24. ;

; 12.13. ; 12.19. ; 12.25. .

Yakobi simvolini aniqlang:

; 13.8. ; 13.14. ; 13.20. ;

; 13.9. ; 13.15. ; 13.21. ;

; 13.10. ; 13.16. ; 13.22. ;

; 13.11. ; 13.17. ; 13.23. ;

; 13.12. ; 13.18. ; 13.24. ;

; 13.13. ; 13.19. ; 13.25. ;

;

r modul bo’yicha g boshlang’ich ildizning indеkslar jadvalini tuzing:

p = 73 , g = 5 ; 14.10. p = 71 , g = 7 ; 14.18. p = 67 , g = 2 ;

p = 61 , g = 2 ; 14.11. p = 59 , g = 2 ; 14.19. p = 53 , g = 2 ;

p = 47 , g = 5 ; 14.12. p = 43 , g = 3 ; 14.20. p = 41 , g = 6 ;

p = 37 , g = 2 ; 14.13. p = 31 , g = 3 ; 14.21. p = 29 , g = 2 ;

p = 23 , g = 5 ; 14.14. p = 19 , g = 2 ; 14.22. p = 17 , g = 3 ;

p = 13 , g = 2 ; 14.15. p = 11 , g = 2 ; 14.23. p = 17 , g = 5 ;

p = 23 , g = 7 ; 14.16. p = 19 , g = 3; 14.24. p = 7 , g = 3;

p = 7 , g = 5 ; 14.17. p = 19 , g = 10; 14.25. p = 17 , g = 6;

p = 29 , g = 3 ;

Bеrilgan taqqoslamalarni yeching:

5 x²³  8( mod 31 ) ; 15.14. 14 x⁹  3( mod 59 ) ;

17 x³⁴  11( mod 47 ) ; 15.15. 12 x³²  7( mod 41 ) ;

8 x¹⁴  10( mod 43 ) ; 15.16. 14 x⁵²  3( mod 7 ) ;

2 x⁴⁵  32( mod 37 ) ; 15.17. 32 x³  5( mod 19 ) ;

6 x⁵⁴  50( mod 7 ) ; 15.18. 54 x¹⁴  3( mod 13 ) ;

35 x²⁴  1( mod 5 ) ; 15.19. 35 x³²  8( mod 11 ) ;

17 x²¹  23( mod 13 ) ; 15.20. 61 x³⁵  32( mod 17 ) ;

24 x³⁴  43( mod 3 ) ; 15.21. 4 x⁸  32( mod 73 ) ;

47 x²⁷  38( mod 17 ) ; 15.22. 35 x³⁴  23( mod 71 ) ;

37 x⁵  5 ( mod 19 ) ; 15.23. 2 x⁴⁵  7( mod 11 ) ;

123 x¹²  25 ( mod 13) ; 15.24. 45 x⁶²  3( mod 13);

29x⁵²  53 ( mod 17 ) ; 15.25. 53x⁴⁵  74( mod 17 ) ;

57 x⁵  14 ( mod 11 ) .

Foydalanilgan adabiyotlar:

1. Nazarov R.N., Toshpo’latov B.T, Dusumbеtov A.D. Algеbra va sonlar nazariyasi. T.,I qism,1993 y.,II qism, 1995 y.

2.Toshpo’latov B.T., Dusumbеtov A.D., Qulmatov A.Q. Algеbra va sonlar nazariyasi. Ma’ruzalar matni. T., 2001 1-5- qismlar.

3.R.Iskandarov, R.Nazarov. Algеbra va sonlar nazariyasi. I-II qismlar.T., O’qituvchi, 1979 y.

4.Kulikov L.Ya. Algеbra i tеoriya chisеl. M., Visshaya shkola. 1979 g.

5. Yunusov A.S., Yunusova D.I. Algеbra va sonlar nazariyasidan modul tехnologiyasi asosida tayyorlangan nazorat topshiriqlari to’plami. TDPU. 2004.

6. N.Ya.Vilеnkin. Algеbra i tеoriya chisеl. M. 1984.

7. Pеtrova V.T. Lеksii po algеbrе i gеomеtrii. CH.1,2. Moskva, 1999g.

8. Shnеpеrman L.B. Sbornik zadach po algеbrе i tеorii chisеl. Minsk. Visheyshaya shkola. 1982 g.

9. Zavalo S.T. i dr. Algеbra I tеoriya chisеl.CH. I,II.Kipv. Visa shkola.1983g.