Question 4 Solve the following system of congruences and in addition, prove that there exists only one solution according to modulo [6. 8. 20] x = 5(mod6) I = 7(mod8) x = 3(mod20)

Q: Find all the solutions of the congruence equation x6-2x5= 35 (mod 6125).

A: Consider the given congruence equation. x6-2x5≡35mod 6125. Now, the prime factorization of 6125 is:…

Q: Find all solutions of the congruence 8x ≡ 4 (mod 12)

A: Step 1: Divide by the greatest common divisor (GCD)The GCD of 8 and 12 is 4. We can divide both…

Q: Find a primitive root of 29 Solve x6 = 4 (mod 29)

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

A: 7x≡5 (mod52)---(1)

Q: The least positive integer solution for the congruence 2x = 14 (mod 18) is Answer:

A:

Q: 2.23 Find all four solutions to the equation x²10 (mod 35).

A: The given equation is: x2-1≡0 mod 35 We have to find all four solutions to the given equation.

Q: Find the value of 786 (mod 13) using Fermat's Little Theorem. Remember, x (P - 1) = 1 (mod p) 786 =…

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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: Use Hensel's Lemma to find a solution to the following congruence: a +3 x + 3 = 0 mod 54.

A: Let f(x) be a polynomial , p is a prime number . If x=a is a solution of congruence equation…

Q: x² - 2x = 8(mod19) X= (mod19)

A:

Q: X = 17 (mod 21) X= - ) 8 Cmod 25

A:

Q: Find all the solutions of 15z = 27 (mod 18).

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Q: Simplify (98 +31)(mod 7).

A: To simplify (98+31)(mod7), first perform the addition inside the parentheses and then find the…

Q: olve the congruence8x= 16 (mod 424).  If none exists, explain why.  If there are one or…

A: The given equation is: 8x≡16mod 424

Q: solution to the congruence equation (3x + 12) = 7 mod 10

A: Given :  3x+12=7mod 10⇒     3x=7-12 mod 10⇒     3x=-5 mod 10⇒     3x=5 mod 10        -5 mod 10 =5⇒…