13. In Z26, it is true that 3-9 = 1,5-21 = 1, 7-15 = 1, 11-19 = 1, and 17-23 = 1 mod 26.Use this information to solve 15x + 3 = 7 mod 26.[Your answer should be of the form x = a mod 26 for a € Z26.]

Modulo is defined as the remainder getting when one number is divided by another number. Modulo is…

Answered: 13. In Z26, it is true that 3-9 = 1,…

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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please don't provide hand wrtten solution....
In the following question: " Let a, b ∈ Z. Show that if a ≡ 5 (mod 6) and b ≡ 3 (mod 4), then 4a + 6b ≡ 6 (mod 8)." why do we ignore the -6 when substituting the variables of a and b, if we expand "4a + 6b ≡ 6 (mod 8)" we get (4a+6b)-6=8y, when we substitute we have to end up with the 8y right? Im just confused why the -6 is ignored?
10
1. Solve 5x = 1(mod 19) 2. Use the EEA to find integers x and y such that: 300x + 222y = gcd(300,222) 3. Which of the following numbers are prime? Show why. a. 1527 b. 15277
1. For each solution. JX² = -1 (mod 397) (397 is prime) CO congruence determine whether there is a x² +8x + 14 = 0 (mod 37) ししし iii) x² = 785 (mod 787) (787 is prime)
2. Solve the simultaneous congruences x = 4 (mod 5) and 2x = 3 (mod 7)
8. Solve 3x² + x + 8 元 0 (mod 11) and 3.x² + x + 52 = 0 (mod 11).
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5. Use the baby step, giant step method to solve 2k = 7 mod 13

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13. In Z26, it is true that 3-9 = 1, 5-21 = 1, 7-15 = 1, 11-19 = 1, and 17-23 = 1 mod 26. Use this information to solve 15x + 3 = 7 mod 26. [Your answer should be of the form xa mod 26 for a € Z26.]