A. Find the value of x. 61 = x ( mod 7) 1. 71 = x ( mod 8) 2. 5) 89 = (x + 3) ( mod 4) 78 + x = 3 ( mod 3. В. 1. What is the remainder when 20212021 divided by 2020? is 4.

Q: The statement a ≡ b (mod n) is called a congruence.

A: Given that  The statement a ≡ b (mod n) is called a congruence.

Q: Use trial and error to find all replacements for x that are less than the modulus that make the…

A: To find- Use trial and error to find all replacements for x that are less than the modulus that make…

Q: Write a proof that proves the Union Un an element of natural numbers (-1/n, 2-1/n)=(-1, 2). Also…

A: The given interval is (-1/n,2-1/n) where natural number n belongs to positive integers. So that we…

Q: **: 2 is a primitive root mod 13 : Find a solution to x^5 ≡ 11 mod 13 you have to explain well how…

A:

Q: Solve the congruence 2x + 3 = 11 (mod 7). (Select all congruence classes below (modulo 7) that…

A:

Q: x^2 ≡ 1 (mod 105)

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

Q: P (A) a, P (B) b and P (P (AB)- c then the expression of P (A'B')in erms of a, b and c is:

A:

Q: (7) (a) Find the order of a modulo 7 for a = 1, 2, 3, 4, 5, 6.

A:

Q: Encrypt the message STOP POLLUTION by translating the letters into numbers, applying the given…

A: According to the given information, it is required to first encrypt the message STOP POLLUTION by…

Q: Find all Pnterers x such that 5x=12 (mat) LoxE 4 (mad) 7x=16 (modlo) and 1o00s x3000

A:

Q: If x^677 ≡ 3 mod 2020, find x.

A: We have   x677≡3mod2020⇒x677-3=2020m   where m is integer different values of m we get different…

Q: Show that PLEU FUG) = P(E) + P(F) + "P(G) - PLENF) - P(ENG) - P(FNG) + P(ENENG)

A: There are three events. These are E, F, G. The objective is to show that,

Q: 3x = 1 (mod 6)

A: 3x≡1 (mod 6) ⇒ 3x-1≡0 (mod 6)This means 3x-1 is divisible by 6.

Q: Find all values of x (using congruent notation) for 35x ≅ 3 (mod 89)

A:

Q: True or False 18 ≡ 12 (mod 3) is not a true congruence.

A:

Q: Which of the following linear congruence has 1 incongruent solution? (a) 3x = 9 (mod21) (b) 14x = 12…

A: The solution is given as

Q: Find  mod (40, 7) and div (40, 7).   mod(40, 7)=? div(40, 7)=?

A: 1) mod(40,7)  is the remainder when 40 is divided by 7we know that 7×5 =35  and 7×6=42as 7×6=42 is…

Q: Inverse of 9 modulo 23 is -18 -17 18 17 Windows by

A: Solution: We have to find the inverse of 9 modulo 23. Let x be the required inverse. Then, 9x≡1mod…

Q: Let n be a positive integer. Using congruences, show that 3n+3 +23n+3 is divisible by 7.

A:

Q: Evaluate (i^{i})^[i] and i^{-1}. (Hint: They might be different) **I got a -i for the second one by…

A: Step 1: Step 2: Step 3: Step 4:

Q: Simplify (42-67)(mod 3). (42-67)(mod 3) = (mod 3)

A: Here we have to find the value of(42-67)mod 3

Q: True or False : 4x ≡ 12 (mod 10) ⟹ x ≡ 3 (mod 10)

A:

Q: What letter replaces the letter K when the function f (p) = (7p + 3) mod 26 is used for encryption?

A:

Q: Write down the formal definition of the real nunmbes

A: The solution is given below

Q: Find 2's complement of 001011011001100

A:

Q: Dividing a congruence by an integer always produces a valid congruence False () True

A: Given the  The statement is true or false

Q: Prove that (-1+ iB)" + (-1- i3)" has either the velue 2t! or the value if a B any integer (positive,…

A:

Q: 5x² + 3x = 3(mod17) X = (mod17)

A: Given that 5x2+3x≡3 (mod 17)x(5x+3)≡3 (mod 17)x≡3 (mod 17)  or   (5x+3)≡3 (mod 17)x≡3 (mod 17)  or…

Q: = solve (y² + 2y² + ay +18) dx. (5x³y²-x²y + 17x²) dy

A:

Q: expand 7q(q-2)

A: To expand: 7qq-2 We know that: a(b+c) = ab +ac

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}

A:

Q: If Z=1//2+j/v2 then the value * ?=of conjugate of Z^5

A: According to Euler, the complex number of the form cosθ+isinθ can be written as eiθ. The conjugate…

Q: てheorem' Let p be aprime number, a integer (ap)-1 0nd pacitive integer. In this cose; ) #1 (mod p)…

A: We need to use the above given two theorems to find the solution for the given congruence

Q: Please poove 18 ŏ bound of (३5) fश्ठ also proove ppes an sup13,5)%35

A: (.) Upper bound:    "A number that is greater than or equal to any number in a non-empty subset of ℝ…

Q: 12 2» de Jo Evaluate

A: We have to solve integration

Q: 5(mod

A: