7x + 3y = 10 (mod 16) 2x + 5y = 9 (mod 16)

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

A:

Q: Find the answer of -16 mod 5

A:

Q: Solve for x: 7x = 3 mod 11

A:

Q: x^2 ≡ 1 (mod 105)

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

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

A:

Q: Find all integer solutions satisfying all the equations given. 5x =1 mod 39 3x =1 mod 25 4x =1 mod…

A: Concept :.   *   ax =6 mod n                           g (d (a,n) = d (let)…

Q: Let ab5c be all four-digit multiples of number 36 with different digits. If someone found 7 numbers…

A: Let ab5c be all four digit multiples number 36 with different digits.   As 36= 4x9, so the number…

Q: (i)Find the inverse of 5(mod9)     (  ii)Hence or otherwise solve simaltaneous equation…

A:

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 We need to solve x2≡186 mod 101 and how many solution exists.

Q: How would I solve for n and m (without a calculator)? Please explain. 5" = 3( mod 97) 5m = 7( mod…

A: to find the value of m , n when 5n≡3 mod 975m≡7 mod 97 (i) we can write 5n≡3 mod 97 as   5n=97s+3…

Q: 10. (8 points) Solve 3x 2, (mod 7) or show that no solution exists.

A: Solution: The objective is to find the solutions of 3x≡2 (mod 7)

Q: True or False Statement 12 ≡ 7 (mod 5) is equivalent to 22 ≡ 7 (mod 5).

A:

Q: 3. Solve the system of congruences x = 1(mod 5) x 2(mod 6) r= 3(mod 7)

A:

Q: Solve 57x ≡ -3 (mod 50) for x

A:

Q: 3x = 11 (mod 20)

A:

Q: X=4(mod nod 13) X2-7(mod 15)

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: x3-3x2+27 is congruent to 0 (mod 225)

A: Consider the following problem  x3-3x2+27≡0mod 225 Prime factorization of 225 is 32×52 Now,…

Q: 2n3 + 3n2 +n ≡ 1 (mod 6) Select one: True False

A:

Q: Solve for x : 5x ≡ 7 (mod 6).

A: Here remainder is 7 and modulus is 6 we can write it as  5x-7 =6n          Where  is an positive…

Q: 4. Using your work from the earlier parts or independently find: (a) mod 8 (b) + mod 23 17 (c) mod 7

A: Given

Q: solve the congruence of  6x=4 mod 10  aolve the conguence of 341x=2941 mod 9

A:

Q: solve for x^2 = 1 mod 8 and x^2 = 1 mod 10

A: Solution...

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

A:

Q: where _13-4 mod 13

A:

Q: Number of solutions of the equation 3x - 2x + 5x2 + x+2= 0 under modulo 5 is'are OB. OD 3

A: Consider the given equation, 3x4 - 2x3 + 5x2 + x + 2 = 0 The set modelo 5 is, ℤ5={0, 1, 2, 3, 4}…

Q: Solve 8 2x +34 (mod 13) 3x +4y = 2 (mod 13) الطرف Using elimination.

A:

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

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

Q: Solve the system of congruence x ≡ 3(mod6) and x ≡ 4(mod7) using the method of back substitution.

A: System of congruence equations

Q: 11. Solve the congruence 4x = 5 (mod 9).

A:

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: Solve the congruence: 6x ≡ 4 (mod10)

A: The congruence could be written as,

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: The value of 2*5 where is defined as Modulo 7 is? 2. 3 3 4. 2

A: Modulo function: a modulo b gives the remainder after dividing a by b.

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 mx = 1 (mod n) has a solution, then nx= 1 (mod m) has a solution. Select one: O True False

A:

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 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: True/False: If 10x = 20 (mod 8) holds, then x = 2 (mod 8) must be true.

A: True.

Q: Solve the system of congruences 2x + 6y = 3 (mod 15) 3x + 7y = 6 (mod 15)

A:

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

A:

Q: 3x is congruent to 2 mod 13

A:

Q: ulus) 1) Solve the following congruences system. 5x +4 = 12 (Mod 7) 14x - 3 = 19 (Mod 5) 2) Prove…

A:

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

A: We need find multiplicative inverse of 9 in z/23z

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

A:

Q: how did they get 9x^2 from (x^4)/(5x^2)mod11 ?

A: Use of z11[x],

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

A:

Q: 12x ≡ 18 (mod 15) has exactly 3 distinct solutions modulo 15 Select one: True False

A: 12x ≡ 18 (mod 15) has exactly 3 distinct solutions modulo 15 Select one: True False

Q: 17≡ 7 (mod  2) ,true or false?

A: