If a = 1 (mod n) and b = 1 (mod n) then a - b = 0 (mod n) اختر واحدا: 2 3

Q: Solve the linear congruence 7x = 13 (mod 19).

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Q: Any number n is congruent to the sum of its digits modulo 4. Select one: True False

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Q: Find the answer of -16 mod 5

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Q: If a= b (mod n) and gcd (a, n) = d, then gcd (b, n) = d :Select one True False

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Q: 4. Find all numbers between -50 and 50 which x mod 13 = 3

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Q: TRUE or FALSE: 1. If a is congruent to b (mod m), then a^k is congruent to bk (mod m) for every…

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Q: find x, where x= 9753 (mod 120) and -120<x<0

A: Ans: -87

Q: What are the FOUR values of x that will satisfy: x ≡ 4 mod 5 & x ≡ 3 mod 7 please show your…

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Q: Find all whole number solutions of the congruence equation.  2x+1≡ 5 mod 4 3x+1≡ 4 mod 9

A: The given problem is to find the whole number solutions for given system of linear congruence…

Q: If gcd(a, n) = 1, then the congruence ax = b modn has the solution x = - ba®(n)-1

A: Given that gcd(a,n)=1. We need to check whether ax≡b mod n has the solution x=ba∅(n)-1

Q: 2. If a = 1 (mod p), then a=1 (mod p). Select one: True False

A: If , then . The truthfulness of the given statement can be proved by taking an arbitrary value for…

Q: he linear congruence 132x ≡ 76 (mod 100) has a solution. Select one: True False

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Q: Compute the addition modulo operation 3+2 2 0. 1 3 O O

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Q: (-130 mod 20·265 mod 20) mod 20 ?

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Q: If m = 2* is a power of 2, explain how you could use repeated squaring to compute am (mod n) for all…

A: a) We have m = 2k. First we illustrate the method of repeated squaring to compute am (mod n). Then…

Q: (9) Find all prime numbers p for which both equations X²-2 0 mod p and have solutions. X²-3 0 mod p

A: Concept: The quadratic congruence: x2≡a(mod p) , where gcd(a,p)=1 Has a solution if (ap)=1 That is a…

Q: Find all solutions to x^2=6 mod 143, note that 143=11*13 (I solved x^2=133 mod 143, but i'm not sure…

A: It is required to find all the solutions of x2=6mod143 Given that 143=11×13 Where 11 and 13 are…

Q: The set {0,5,6} is closed under Mod(10)

A: To check if { 0 5, 6} is closed under mod(10)

Q: What prime numbers are squares in mod 17? (Include primes that are larger than 17). What primes p…

A: Since the squares less than 17 are 1, 4, 9, 16 then the prime numbers that are squares in mod 17 are…

Q: Is it true that 90 ≡ 64 (mod 13)?

A: As given equation 90≅64(mod 13) is False.

Q: Determine the number of primitive roots modulo 23.

A: Solution

Q: What is 2 ^32 mod (5)?

A: mod is the function whose output is always positive. mod is represented by .

Q: How do I prove this: Show that if x ≡ 1(mod n), then x^2 ≡ 1(mod n) and x^3 ≡ 1(mod n) and how to I…

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Q: 8. How many positive divisors does 2000= (2^4)(5^3) have?

A: Note: Hey there! Thank you for the question. As you have posted multiple independent questions, we…

Q: determine what number the sum is congruent to in mod 3, 6+4 = __ (mod 3)

A: First we add the numbers, then check for the remainder on dividing the result by 3 and that will be…

Q: Which of the following are true modulo 12? (1) Does 5z = 6 mod 12 have a solution? How many? (2)…

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Q: To Determine the value that 46 is congruent to IN modulo 7

A: Note that, If a and b are integers and n &gt; 0, then a ≡ b (mod n) to mean n|(b − a) and It can be…

Q: The remainder when aa is divided by 77 is 22 and the remainder when bb is divided by 77 is 55. (So a…

A: Given:          a≡2 mod(7)  and b≡5 mod(7)

Q: Find the order of 4 modulo 49.

A: Evaluate order of 4 modulo 49.

Q: State whether True or False: If A and B are integers and A ≡ 3 (mod 3) and B ≡ 2 (mod 6) then A+B ≡…

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Q: If 3x = 6 mod 9, when -2 <x< 8. Then O x=(-1, 3, 5} x=(-1, 2, 5} O x=(-1, 2, 3} O x=(-1, 5, 6}

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Q: Inverse of 9 modulo 23 is 18

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Q: Suppose that 3x ≡ 2 (mod 5). Find the remainder when x is divided by 5; in other words, compute x…

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Q: Find all solutions to the congruence13x−3 = 4 (mod 26). If none exists, explain why.Your…

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Q: If 3x = 6 mod 9, when -2 < x< 8. Then O x={-1, 3, 5} x-1, 2, 5} O x=(-1, 2, 3} O x=(-1, 5, 6}

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Q: 3

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Q: Suppose n is a large odd number. You calculate 2(n-1)/2 = k (mod),  where k is some integer k is not…

A: Given that 2n-12≡kmodn Take the square on both sides, 2n-12≡kmodn2n-12·2≡k2modn2n-1≡k2modn (a) The…

Q: (a) What is 84 (mod 9)? (b) What is 52 (mod 5)? (c) What is -4 (mod 10)?

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Q: Number theory

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Q: Which are true for modulo 12? 1.) Does 5x ≡ 6 mod 12 have a solution? How many? 2.) Does 4x ≡ 6 mod…

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Q: 3x is congruent to 2 mod 13

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Q: Compute 22 mod 3, 24 mod 5, 26 mod 7.  What do you notice?  Does Fermat predict your answers? (If…

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Q: If a (mod 0) = a, How would you interpret the congruence a ≡ b (mod 0)?

A: According to the given information, it is given that:

Q: 3 congruent to 1 (mod5) 2 congruent to 3 (mod 7) 5 congruent to 11 (mod3)

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Q: Determine four values of x that will satisfy: x ≡ 4 mod 5 & x ≡ 3 mod 7 please show your solution

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Q: true or false? explain this: 2 mod 5 ≡ 7 mod 5

A: a mod n  ≡ b mod n if n divides (a-b).

Q: (2) If a = b modn and a = b mod m and ged(m, n): 1. then a =b mod mn.

A: The greatest common divisor of two or more integers, which are not all zero, is the largest positive…

Q: Number theory

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Q: What are the FOUR values of x that will satisfy: x=2 mod 4 & x=3 mod 6 please show your…

A: Given: x≡2 mod 4  &amp; x≡3 mod 6   x≡a(mod m1)x≡b(mod m2) has a solution if and only if…