Quèstion 5 m = 37 satisfies one of the following congruence 53x 25 = 5 (mod m) 19x374 2 (mod m) 61x15 =4 (mod m) 23 x 39 = 3 (mod m)

Q: 5. 2x 15 (mod 17) 6. 4x 6 (mod 17)

A: According to our guidelines we can do at most three subpart of a question at a time. So please post…

Q: For any linear ODE, the sum of any two solutions is also a solution. Select one: True False

A: For any linear ODE, the  sum of any two solution   is also a solution.

Q: x^2 ≡ 1 (mod 105)

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

Q: solve the congruence 2²-7x+6=0(mod3³.7³)

A: Given congruence: Objective: Solve the congruence equation and find the solutions for  modulo .

Q: Solve the con Congruence 1x²=6 (mod17)

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Q: 2r = 3 4x = 2 3x 2 (mod 5) (mod 6) (mod 7).

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Q: congruences 4* = 13 (mod_17) and 54 (mod 19).

A: Given congruences are: 4x≡13mod 175x≡4mod 19 We have to solve the given exponential congruences.

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

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Q: Solve the system 3x + 2y = 5 2x + 7y= 9 mod 17 mod 17

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Q: Solve the congruence17x−3 = 4 (mod 26).

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Q: How could we calculate the congruences 10^x ≡ 243 mod 19^2 with 14x^15 ≡17 mod 19. The answer of mod…

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Q: x43 = 47 (mod 713)

A: Step:-1 By Chinese remainder Theorem (CRT),  x43 ≡ 47 mod 713 if and only if x43 ≡47 mod 23 ⇒x43 ≡1…

Q: x = 2 (mod 5) 2r = 22 (mod 8) 3x = 12 (mod 21) (i) How many solutions does it have lying between 0…

A: i)Given thatNotice first that the moduli are pairwise relatively prime, Therefore, we can use the…

Q: 1. Solve the Congruence x^5 ≡ 2 (mod 7)   2. Solve the congruence x^7 ≡ 10 (mod 23)   Show work…

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Q: Question 13 3 = 5 (mod2) OTrue O False

A: We have to check that the given statement is true or false.

Q: Simplify the following expressions by hand and show your work: 23^421 mod 31 57^2024! mod 43…

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Q: -3x = 4{mod8}

A: 3x = 4 (mod 8)  We have to find all integral value of x.

Q: Solve each of the following congruences: (a) x = 6 (mod 10); x = 11 (mod 15) (b) x = 3 (mod 21); x =…

A: Sol:- (a) To solve x ≡ 6 (mod 10) and x ≡ 11 (mod 15), we can use the Chinese Remainder Theorem.…

Q: Determine the system of linear congruences which yeild all the square roots of 31 modulo 33.

A: Please find the answer in next step

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: (a) Find all solutions r to the congruence 341x = 16 mod 912

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

Q: System of congruences (smallest +integer for answer): x = 3(mod 7) x = 4(mod 9) x = (1 mod 6)

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Q: If possible, solve the following linear congruences. (a) 42x = 1014 (mod 91) (b) 42x = 1015 (mod 91)

A: If possible, we have to solve the following linear congruences.

Q: Find the solution of the following equations: 6x = 1(mod 33), 7x 1(mod 9)

A: If the given congruence equation is:.It is known that if a and m are relatively prime, then the…

Q: If 19 =7 (mod 6) and 27 =3 (mod 6) then 19x 27 = 7+3 (mod 6) 19+27 = 7+3 (mod 6) 19+27 =7x 3 (mod 6)…

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Q: -) Find the solutions, if any, of each congruence. 21x 10 (mod 35) 9x = 15 (mod 21).

A: We know that, ax≡b mod n has solution if and only if gcd(a,n) divides b.

Q: 2) Solve the following linear congruences: 14x = 91 (mod 189) 24x = 56 (mod 88)

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Q: Solve the congruence x² = 9 (mod 600).

A: Given congruence is x2≡9 mod 600

Q: Question 2 Solve the linear congruence 19x =7 (mod 90127)

A: We have to Solve given linear congruence by following way.

Q: find the congruence for the following congruence equations: (1) 18x=3 (mod47)

A: First and second question are independent .So According to guideline I am solving first one.The…

Q: 3

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