4. (a) Solve the set of congruences х 1(mod 3), x= 2(mod 4), x = 3(mod 5).

Q: The equation 20x=30 (mod 70) has: 10 non-congruent solutions modulo 70 None of these no solution…

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Q: The equation 82r = 12 (mod 13) has O 1 incongruent solution modulo 12 O 4 incongruent solutions…

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

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Q: 1. Solve the following linear congruence using a systematic method: 167x = 241 (mod 199) Present…

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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: 7) Solve the system of linear congruences below: x = 2 (mod 7) x = 10 (mod 15) x = 9 (mod 26)

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

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Q: 1. Find all simultaneous solutions of the congruences: (a) X= 3 mod 5 x= 4 mod 6

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Q: Find the smallest positive integer that solves both of the given congruences.   x ≡ 3(mod4​), x ≡ 5…

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Q: 2x = 4 (mod 8) a. has no solution b. has infinite solutions c. has a unique solution modulo 8 which…

A: Here 2x≡4 (mod 8). Hence 2x=4+8k, for some integer k. Dividing by 2, x=2+4k, for some integer k.…

Q: Solve the congruence3x−7 = 2 (mod 16). Your solution should be positive and reduced modulo16.

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Q: 8. Find the solutions to the given system of linear congruence. x= 1 (mod 3) x = 3 ( mod 5) x = 4 (…

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Q: The equation 21x=49 (mod 70) has: 6 non-congruent solutions modulo 70 7 non-congruent solutions…

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Q: Find the solutions of the congruence 15x2 + 19x ≡ 5 (mod 65)

A: The given equation is: 15x2+19x≡5(mod 65)

Q: Find all the non-congruent solutions to  4x ≡ 6(mod 21)  express solutions using the stand…

A: Introduction: A linear congruence is generalized as ax≡bmod n. The greatest common divisor of a and…

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 x2+3x+2 is congruent to 0 (mod 55)

A: 55=5×11 and gcd(5,11)=1, hence they are co-prime.The given system of equation x2+3x+2≡0mod 55 is…

Q: The equation 15x=30 (mod 50) has: 5 non-congruent solutions modulo 50 6 non-congruent solutions…

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Q: Show that th equation x" + y² = z" (mod 5) has nonzero solutions in Zz if and only if n is odd.

A: Given: xn+y2n≡zn(mod 5)

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: 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: 2. Find the largest negative x € Z that simultancously satisfies 4x = 9 (mod 5) 2x = 0 (mod 6) x =0…

A: Given : 4x = 9 (mod 5) 2x = 0 (mod 6) x = 0 (mod 4)

Q: The equation 12x=24 (mod 48) has: * no solution modulo 48 24 non-congruent solutions modulo 48 None…

A: Given the equation 12x≡24(mod 48)

Q: Exercise 3. 3x +1= 2 (mod 9) a has no solution modulo 9 b. has six non-congruent solutions modulo 9…

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

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Q: The equation 82x = 12 (mod 13) has O 1 incongruent solution modulo 12 O 4 incongruent solutions…

A: First Option Is Correct Answer.

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

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

A: The given congruence equation is                                             3x+12≡7 mod 10

Q: The equation 82x = 12 (mod 13) has O 1 incongruent solution modulo 12 O 4 incongruent solutions…

A: The given equation is 82x = 12(mod 13)

Q: Solve the system of congruence's x = 2 (mod 3), x = 4 (mod 5), x = 1 (mod 7)

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

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Q: 3

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Q: Number theory

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Q: Find all whole number solutions of the congruence equation. 2x+3 ≡ 8 mod 12

A: Given that  2x+3 ≡ 8 mod 12  we have to find the value for 'x'

Q: Number of solutions for the congruence equation x^2 + 2x + 1 = 0(mod 52) is

A: The given congruence equation is x2+2x+1 = 0(mod 52)

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

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Q: The equation 30x≡24 (mod 48) has: * 24 non-congruent solutions modulo 48 no solution modulo 48 None…

A: ax≡b (mod m) has solutions if and only if gcd(a,m) divides b. Moreover the number of non-congruent…

Q: Number theory

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Q: 10. Find all solutions of the system of congruencies x = 2 mod 3 x = 4 mod 5 x = 3 mod 7

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Q: The equation 21x = 49 (mod 77) has: O no solution modulo 77 only 11 non-congruent solutions modulo…

A: Here we have given equation,  21x = 49 (mod 77)    Let a, b and m be integers such that m>0 and…

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 equation 21x = 49 (mod 77) has: O no solution modulo 77 only 7 non-congruent solutions modulo 77…

A: Solution

Q: Find all whole number solutions of the congruence equation. 4x+6 ≡ 5 mod 8

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Q: How do I use the Chinese Remainder Thm. to solve this system of congruences?? x ≡ 2 (mod 3) x ≡ 6…

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

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Q: Solve the Diophantine equation 7x + 5y = 43 by  rst solving the congruence 7x = 43 (mod 5), which is…

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