Find 123 (mod 11) + 321 (mod11).

Q: Given 6x + 2 ≡ 101 (mod 7), find an integer z such that 2x ≡ z (mod 7)

A:

Q: 2x = 29 (mod 27)

A: 2x=29-1  mod 27 Now, simplify the given relation, 2x=129  mod 2758x=1  mod 27

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

A:

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

A: Ans: -87

Q: If mx = 1 (mod n) has a solution, then nx = 1 (mod m) has no a solution. Select one: True False

A: We know the definition of Congruence ,  Suppose m be a positive integer , we say that integers a and…

Q: 2. Give an example to show that a? = b2 (mod n) need not imply that a =b (mod n). 3. If

A: Given below the detailed solution

Q: Find 12 ^– 1(mod 17), the inverse of 12 modulo 17

A: Find an inverse of 12 modulo 17 as follows.

Q: Prove that if ax = b (modn) then () x = () (mod ()) where d = gcd(a, n). Apply this result to 5x =…

A:

Q: Name all integers from -100 to 100 that are congruent to -1 modulo 25!

A:

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

A: 7x≡5 (mod52)---(1)

Q: 2X=3 mod 5 Show your work

A: the given congruence equation is 2x≡3mod 5 the general congruence equation is ax≡bmod c…

Q: 1. How many solutions( mod 419) does x = 186 mod 419 have? (Show your work!) 2. How many solutions (…

A: Given: x2≡186 mod 101  To find: Number of solutions that exists. Method Used:  For any, xk≡b mod p,…

Q: 3. Show that ifn = 2 (mod 4), then 9" + 8" is divisible by 5.

A: Here we will prove the given statement.

Q: Solve 57x ≡ -3 (mod 50) for x

A:

Q: Find 1112 mod 13.

A:

Q: (2x + 3 ) ≡ 8 mod 12

A: (2x + 3 ) ≡ 8 mod 12 x + 3 + 9 ≡ 8 +9 mod 12  2x + 12  ≡ 12 +5  mod 12

Q: #5. Suppose that a = 2 (mod 113), and b = 5 (mod 113) What is (a b + 56b + 155) mod 113?

A: given a≡2(mod113),b=5(mod113)a3≡23(mod113)a3b≡235(mod113)56b≡280(mod113)56b≡54(mod113)155≡15mod113)

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

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

Q: Is 7|(15+20): True or False? 28 is congruent to 42 modulo 6: True or False?

A: I am solving these in step 2

Q: The inverse of 3 modulo 7is -2

A: Given statement, The inverse of 3 modulo 7 is -2.

Q: Find the integer that satisfies: 30x4 ≡ 12 (mod 67)

A: Given the expression is, 30x4≡12mod 67

Q: Find all integer values of x for which 3x = 4 (mod 8).

A: given congruence equation 3x≡4(mod 8)

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

A:

Q: Show that 18! ≡ -1 (mod 437).

A: We have to show that: 18!≡-1mod437

Q: Which pairs of the integers -11, -8, -7, -1, 0, 3, and 17 are congruent modulo 7?

A: -11≡3 (mod 7) holds  Since -11-3 = -14 is divisible by 7 and leaves remainder 0. -7≡ 0 (mod 7)…

Q: Determine if x² = 29 mod 541 has a solution.

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 &gt; 0, then a ≡ b (mod n) to mean n|(b − a) and It can be…

Q: Suppose that a = 3 mod 12 and b =7 mod 12 IfC = 3 a – 2 b mod 12 then C =

A:

Q: Does 5x = 6 mod 12 have a solution? How many?

A: As per our guidelines we are supposed to answer only One question  if there are multiple questions…

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 ≡…

A:

Q: What is the result of: 6(40 – 13) (mod 11) The result is 8

A: Given 6(40-13)(mod 11)

Q: The order of 5 mod 17 is

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

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

A:

Q: Find (177 mod 31 + 270 mod 31) mod 31. Show your wor-

A:

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

A:

Q: Is 27 = 31 mod 5 true or false?

A: False

Q: Find all solutions of 3* = 17 (mod 224)

A:

Q: Show that if x mod 8 = 1, then (3x −5) mod 6 = 4.

A: Solution

Q: Find 2025-3 (mod 212). (Enter the least non-negative integer.)

A: To Find: 2025-3(mod 212) and enter the least non-negative integer.

Q: The equation 12x=24 (mod 48) has:

A: ANSWER IS 12 NON  CONGRUENT SOLUTIONS MODULO 48

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: 4. Find 2001 (mod 205). (Enter the least non-negative integer

A:

Q: What is the smallest positive integer x in the equarion: 1=3x+2(mod 7)?

A: We have to solve the equation 1 = 3x + 2 (mod 7)⇒1 - 2 - 3x = 0 (mod 7)⇒-1 - 3x = 0 (mod 7)⇒3x = - 1…