If positive integers are chosen at random, what is the minimum number you must have in order to guarantee that two of the chosen numbers are congruent modulo 3.

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

A:

Q: if b is modulo m and a is another unit with a=b mod m, we say that d is the---------of a modulo m to…

A: As with such a large amount of concepts we are going to see, congruence is straightforward, perhaps…

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

A:

Q: x^2 ≡ 1 (mod 105)

A: Given: x2≡1(mod 105) To Solve: The given congruence  x2≡1(mod 105)

Q: Show that 2 is a primitive root modulo 3" for all n > 1.

A: To prove that 2 is a primitive root modulo 3n for all n≥1.

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: Any two integers are congruent modulo .when they are both even or both odd. Least common multiple…

A: Answer : smallest prime n=2

Q: Find the smallest positive integer x that solves the congruence: 7x≡5 (mod52)

A: 7x≡5 (mod52)---(1)

Q: Any two integers are congruent modulo to: not a prime nor composite integer o even integer odd…

A: Let a, b are two integers. Two integers a, b are congruent modulo to n (where n is an integer) if…

Q: Any two integers are congruent modulo .. when they are both even or both odd. Least common multiple…

A: Given a statement

Q: Furthermore, any two solutions x and y are congruent modulo n¡n2 · Solve the following systems of…

A: NOTE: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: The least positive integer solution for the congruence 2x = 14 (mod 18) is Answer:

A:

Q: For which positive integers a is the congruence ax4 ≡ 2 (mod 13) solvable?

A:

Q: Let p be a prime with p ≡ 3 (mod 4), and suppose that q = 2q + 1 is also prime. Determine if 2 is a…

A: let p be a prime with p≡3mod 4 and suppose that q=2p+1 is also prime determine if 2 is a square mod…

Q: Find the least residue of 448 modulo 7

A: Given problem is : Find the least residue of 448 modulo 7

Q: the number of incongruent solution of the congruence 8x 10(mod6) is:

A:

Q: Find all the whole number solutions of the congruence equation.x x 5 mod 9

A: The objective is to find all the whole number solutions of the congruence equation.x x = 5 mod 9

Q: Find the least positive integer n that satisfies the congruence 7 ^128 congruent to n (mod13)

A: Given, 7128≡nmod 13 Find the value of n that satisfies the above congruence.

Q: Using Euclid's Algorithm, what is a multiplicative inverse of 23 mod 75 and then solve 23x is…

A:

Q: Find the inverse of 35 under mod 233(if exixts), by using Euclid's Algorithm?

A:

Q: 5. Explain why the congruence r = 2 (mod 4) has no solutions in Z.

A: We have to show that the congruence x2≡2(mod 4) has no solution in ℤ

Q: Given any odd prime p, prove that: 2(p−3)! ≡−1 mod p. (Hint: Start with 2(p−3)!≡x mod p. Then work…

A: Let p be any odd prime number.  So we start with  2p-3!≡x mod p Also we have p-2≡-2 mod pp-1≡-1 mod…

Q: Find a number a such that 70a = 1 mod 17.

A:

Q: suppose a,b ∈ ℤ. Prove that a ≡ b (mod 10) if and only if a ≡ b (mod 2) and a ≡ b (mod 5).

A: In Solution we use divisibility formula that  If a and b are integers, a divides b if there is an…

Q: Find the smallest positive integer for which x mod 3=2 and x mod 4=3   What is the next smallest…

A:

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

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

Q: Suppose Alice and Bob have the same RSA modulus n and suppose that their encryption exponents eд and…

A:

Q: the number of incongruent solution of the congruence 8x = 10(mod6) is:

A:

Q: Find the inverse of 17 mod 26 by using Euclid's Algorithm?

A:

Q: 6), then the congruence has a unique solution modulo p. 11. Show that the congruence x³ = 3 (mod 19)…

A: 11. To prove that the congruence x3≡3 mod 19 has no solutions, whereas x2≡11(mod 19) has three…

Q: Calculate the least residues modulo 5 of 14, 24, 34, and 44.

A:

Q: The order of 5 mod 17 is *

A: Since ϕ(17) = 16 Therefore order can be the divisor of 16 So the order can be 1,2,4,8 or 16

Q: The number of incongruent primitive roots modulo a prime p is: a) Ø(p) b) Фф — 1) с) р—1 O a O b

A:

Q: Find the first few terms of the sequence of pseudorandom numbers generated using the linear…

A: We have to find few terms of the given sequences.

Q: Find all solutions of the congruence x2 ≡ 16 (mod 105).

A:

Q: Use the index system modulo 19 to find all solutions of x³ = 11 (mod 19) and 5ª = 4 (mod 19)

A: In the theory of congruence, Fermat's little theorem is very significant. It says that for any prime…

Q: What sequence of pseudorandom numbers is generated using the linear congruential generator xn+1…

A: Determine the sequence of pseudorandom numbers generated using the linear congruential generator…

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

A:

Q: Find all the whole number solutions of the congruence equation. 3x 8 ≡ mod 11 3x + 12 ≡ 7 mod 10

A:

Q: Find a two digit integer c such that 101c = 1 mod 107. This congruence has a unique solution mod 101…

A: We need to find a digit integer c such that 101c ≡ 1 mod 107. As per the given question, this…

Q: If a = 3 (mod12) then a does not equal 1 (mod6)

A: a=b mod n if and only if n divides a-b Now, we have that a=3mod 12 We need to show that a≠1mod 6 Let…

Q: Prove that for each integer a, if a not equal to 0 (mod 7), then a2 not equal to 0 (mod 7)

A: Consider the provided question,

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. Find all integer solutions to the pair of congruences (if any) x = 1 (mod 2) x = 2 (mod3) x = 3…

A: To Find: Integer solutions to the pair of congruences(if any) x≡1(mod 2), x≡2(mod 3), x≡3(mod 5)…

Q: The linear congruences x = 3 (mod 6), x = 9 (mod 15) has simultaneous unique solution modulo. .....…

A:

Q: (b) Solve the set of congruences 2x =1 (mod 5) x=3 (mod 4)

A: Note:- We’ll answer the first question according our protocol. Please submit a new question…

Q: Find all the integers that satisfy 140x = 133 (mod 301).

A:

Q: Find the smallest positive integer xx that solves the congruence: 11x≡5(mod57)

A:

Q: Any two integers are congruent modulo when they are both evenor both odd. Smallest prime greatest…

A: Any two integers are congruent modulo .. when they are both even or both odd.