II. Determine whether each of these integers are congruent to 7 mod 9 4. 80 5. 106 6. -29

Q: . If 9x = 15 (mod 37), then x mod 37 is 14 17 33 11

A:

Q: 2. If x mod 5 = 4, then x could be O 571 O 400 O 633 O 719

A: Given               x(mod 5)=4

Q: Determine whether each case is true or not : * a. 44 = 13 (mod 3) > b. -55 = 5 (mod 4) → c. 74 = 1…

A: If a and b are integers and n > 0, we write a≡b(mod n) to mean n/(b-a). We read this as “a is…

Q: II. Give FIVE different answers for each of the following. 1. 49 = mod 10 2. 82 = mod 9 3. 100 = mod…

A: 1) Given expression is  49≡______ mod 10

Q: (D) Let s be an integer such that 1 ss < 104651 and 24578° mod 104651 = 3190 Find s and explain how…

A: Let s be the integer such that and Purpose: To find the value of s

Q: mod

A:

Q: 1. Prove or disprove. if alb and bla, where a and b are integers, then a = b.

A:

Q: Which of these integers are in the congruence class of 11 mod 7? (Select all that apply.) O -11 4 6…

A: Which of these integers are in the congruence class of 11 mod 7? (Select all that apply.)

Q: 1. The value of 419 mod 7 is O 5 0 6 O 3

A: Given that 419 mod 7

Q: Prove the assertions below: (a) If a is an odd integer, then a? = 1 (mod 8). (b) For any integer a,…

A: In this question, we have given assertion in terms of congruence modulo here we prove  8(a) if a is…

Q: 7. Calculate each of the following. [from #22, 4.5] b) 971321 (mod 765) a) 2557341 (mod 5681)

A:

Q: - Decide whether each of these integers is congruent to 3 modulo 7. а) 37 b) 66 d) -67 c) -17

A:

Q: which of the below integers is congruent to 6 modulo 12 O 40 O 34 O 30 O none

A:

Q: Consider 3 · 1, 3 · 2, 3 · 3, . . . , 3 · 12 all mod 13, or in other words, the multiples of 3 in…

A:

Q: 29. Decide whether each of these integers is congruent to 5 modulo 17. а) 80 с) —29 b) 103 d) –122

A:

Q: 5. Let a, b, c, and d be any four integers. Assume that 2 divides a, that 3 divides b, that 5…

A: If x divides y, it can be written that y=xk, where k is a constant. In other words, if y is divided…

Q: 5. Let p = 61. Find all incongruent elements modulo 61, that have order: (а) 5 (b) 10 (с) 60

A:

Q: 5. Let a, b e Z and n E Z*. Prove that if a = b(mod n), then gcd(a, n) = gcd(b, n). (Hint: use the…

A: The greatest common divisor (gcd) of two or more numbers is the greatest common factor number that…

Q: 5. Let n be a positive integer, and assume that a and b are integers such that a = b (mod n). Prove…

A:

Q: The remainder in 14 (mod 3) is 3

A: Given that 14 (mod3)

Q: Use the QRT to explain what ' 35 mod 4' means. There exists a unique integer r such that 3514 There…

A:

Q: Find the value of 14147 (mod 1537) 656 657 None of them 659 658

A:

Q: Suppose that a ≡ 9(mod 13) and b ≡ 7(mod 13). Find the integer cwith0≤c≤12suchthatc≡2a2 −6b2(mod13).

A:

Q: mod 1537). 2. Frove the following statements: a) For any integer a, the units digit of a? is 0, 1,…

A: We can solve this expression of  numerical analysis

Q: The value of 538 mod 11 is O 10 O 8

A:

Q: which of the below integers is congruent to 6 modulo 12 O none 40 30 34

A: 30

Q: 25. The value of x in (7x is congruent to 12 mod 17) is O 16 15 9 13 (mod 17)

A:

Q: Which of the following sets is closed under the given operation? O None O (1, 4, 5, 7}…

A:

Q: 20. Are the following statements true or false? Either prove the statement is true or provide a…

A: PART A For the integers a and b, a.b=0(mod 6) This implies that either a=0(mod6) or b=0(mod6). So,…

Q: which one of the following is a congruence ? O 39 = 5 mod 5 O 23 = 4 mod 5 O 29 = 5 mod 15 O 48 = 8…

A:

Q: 12. Decide which of these integers is congruent to 13 modulo 17. a) 81 b) 18 c) -38 d) 83 e) -11

A: Let  x ≈ 13mod (17) Then  x -13 divides 17

Q: III. Determine the value of a such that: 10. a = 11 (mod 21) and 90 s a s 110 11. a = 19 (mod 29)…

A: The given questions are related to congruences. The solution is explained below.

Q: VI. Determine four values of x that will satisfy the following. 16. x = 4 mod 5 & x = 3 mod 7

A:

Q: Which of the following sets is closed under the given operation? O {1, 4, 13} multiplication mod 15…

A: Check for the possibilities for all the options. (a)  Computing the multiplication table,   1 4…

Q: Suppose that a and b are integers, a = 4 (mod 13), and b = 9 (mod 13). Find the integer c with 0 < c…

A:

Q: I. Determine whether each of these integers are congruent to 3 mod 7. 1. 37 2. -17 3. 86

A: We will find out the required solution.

Q: 11. Establish the following relation between Fibonacci and Lucas numbers: L, = un + 2un-1 for all n…

A: Remark: We know that both the Fibonacci numbers and  Lucas numbers are obtained as the sum of its…

Q: Calculate the following: 224 (mod 9) = ?

A: The expression a mod b gives the remainder obtained when a is divided by b. The reminder can be…

Q: In(n² = n(mod 10)), domain is the set of positive integers.

A:

Q: Which of the following satisfies the congruence 4x = 1(mod 5)? O 2 O 3

A:

Q: 5. Decide which of these integers is congruent to 13 modulo 17. a) 81 b) 18 c) -38 d) 83 e) -11

A:

Q: which one of the following is a congruence ? O23 = 4 mod 5 O 39 = 5 mod 5 O 39 = 10 mod 5 O 29 = 5…

A:

Q: x is congruent to 21 mod 8. Then x is None of the option 29 16 24

A:

Q: 15. Decide which of these integers is congruent to 6 modulo 19. a) -32 b) 63 c) -49 d) -11 e) 38

A: Here we have to find which integers are congruent to 6 modulo 19. For this Let us understand a…

Q: 1. Prove each of the following assertions: (c) If a = b (mod n) and the integers a, b, n are all…

A:

Q: Which of the following sets is closed under the given operation? O {1, 4, 13} multiplication mod 15…

A: {0,4,8,16} addition mod 16 And 2/x

Q: Calculate (13, 000 +2)10 (mod 13). Find the omeir lor of 3456 whon dlivided by the following Hint:…

A:

Q: Prove the following statements using either direct or contrapositive proof. 1. Let x,y eZ. If x+y is…

A: Please see the below picture for detailed solution.

Q: 19. Which of the following pairs of integers is NOT congruent to modulo 9? 1 and 10 4 and -32 -2 and…

A: Given  19) Congruent to modulo 9 20) 24 is congruent to 58 mod n 21) 1220(mod 25)