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4. 2x = 3 (mod 5)

4. 2x = 3 (mod 5)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Only need help with #4 & #20. Thanks in advance
2. Follow the instructions in Exercise 1 for the congruence classes modulo 6. Find a solution x E Z, 0 <x< n, for each of the congruences ax = b (mod n) in Exer- cises 3–24. Note that in each case, a and n are relatively prime. 3. 2x = 3 (mod 7) 4. 2x = 3 (mod 5) 5. 3x = 7 (mod 13) 6. 3x = 4 (mod 13) 7. 8x = 1 (mod 21) 8. 14x = 8 (mod 15) 9. 11x = 1 (mod 317) 10. 11x = 3 (mod 138) 11. 8x = 66 (mod 79) 12. 6x = 14 (mod 55) 13. 8x + 3 = 5 (mod 9) 14. 19x + 7 = 27 (mod 18) 15. 13x + 19 = 2 (mod 23) 16. 5x + 43 = 15 (mod 22) 17. 25x = 31 (mod 7) 18. 358x = 17 (mod 313) 19. 55x = 59 (mod 42) 20. 79x = 83 (mod 61) 22. 57x + 7 = 78 (mod 53) 21. 92x + 17 = 29 (mod 37) 24. 82x + 23 = 2 (mod 47) 23. 35x + 14 = 3 (mod 27) 25. Complete the proof of Theorem 2.22: If a = b (mod n) and x is any integer, the a + x = b +x (mod n). (mod n), the
Transcribed Image Text:2. Follow the instructions in Exercise 1 for the congruence classes modulo 6. Find a solution x E Z, 0 <x< n, for each of the congruences ax = b (mod n) in Exer- cises 3–24. Note that in each case, a and n are relatively prime. 3. 2x = 3 (mod 7) 4. 2x = 3 (mod 5) 5. 3x = 7 (mod 13) 6. 3x = 4 (mod 13) 7. 8x = 1 (mod 21) 8. 14x = 8 (mod 15) 9. 11x = 1 (mod 317) 10. 11x = 3 (mod 138) 11. 8x = 66 (mod 79) 12. 6x = 14 (mod 55) 13. 8x + 3 = 5 (mod 9) 14. 19x + 7 = 27 (mod 18) 15. 13x + 19 = 2 (mod 23) 16. 5x + 43 = 15 (mod 22) 17. 25x = 31 (mod 7) 18. 358x = 17 (mod 313) 19. 55x = 59 (mod 42) 20. 79x = 83 (mod 61) 22. 57x + 7 = 78 (mod 53) 21. 92x + 17 = 29 (mod 37) 24. 82x + 23 = 2 (mod 47) 23. 35x + 14 = 3 (mod 27) 25. Complete the proof of Theorem 2.22: If a = b (mod n) and x is any integer, the a + x = b +x (mod n). (mod n), the
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