Use the table of indices modulo 37 to find all solutions to the following congruences. (c) x12 = 11 (mod 37) (d) 7x20 = 34 (mod 37) 12x 23 (mod 37) 5x23 18 (mod 37)

Q: 2. Euclidean Algorithm Use the Euclidean algorithm to find gcd(12345, 678).

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Q: A. 5x = -127 mod 15.

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

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

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Q: 31 = 10 mod 3. :Select one True False

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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: How many square roots of 3 (mod 1001) are there? (Hint: 1001 = 7 * 11 * 13)

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Q: Find 12¹ (mod 17) the inverse of 12 modulo 17

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Q: (a) 142021 = r mod 11 (b) 6150 Er mod 72

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Q: Find all four solutions to x2 =6 (mod 19 x×23) with 1<x< 437.

A: Solution:-

Q: Find all values of x (using congruent notation) for 35x ≅ 3 (mod 89)

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Q: Can you please show me step by step for this math that makes me undertandable. Q: Determine which…

A: (a) For the congruence 4x ≡ 5 (mod 6), we need to find a solution for x such that when 4x is…

Q: 12 = -3 (mod 5) Select one: True False

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Q: Solve the following congruences. Make sure that the number you enter is ≥ 0 and ≤ N-1, where N is…

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Q: (3) If today is Thursday what day of the week will it be 31 days from today? (4) If it is currently…

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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: Simplify (42-67)(mod 3). (42-67)(mod 3) = (mod 3)

A: Here we have to find the value of(42-67)mod 3

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

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Q: (a) 8x = 1 (mod 11) by Euclidean algorithm;

A: We have to solve  by Euclidean algorithm.Note: According to the guidelines we are allowed to solve…

Q: Find an integer A so that: A79 = 7 (mod 277) Please solve step by step thanks!

A: Given an equation. Let's solve for A.

Q: 6. Find all incongruent solutions to each congruence. Show your steps. (a) 135x = 108 (mod 612) (b)…

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Q: Does x2 + 5x congruent to 12 (mod 31) have a solution? (Hint: complete the square)

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Q: Solve each equation for x. (If there is no solution, enter NO SOLUTION.) (a)     x + 8 ≡ 1, (mod 9)…

A: We solve each equation for x.

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

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Q: 3. Solve the following congruences. † (a) 10x = 5 (mod 21) (b) 10x = 5 (mod 15) † (c) 10x = 4 (mod…

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Q: The remainder when aa is divided by 77 is 22 and the remainder when bb is divided by 77 is 55. (So a…

A: Given:          a≡2 mod(7)  and b≡5 mod(7)

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

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Q: Solve each of the following congruences. Make sure that the number you enter is in the range [0,…

A: (b) 58x = 130 (mod 182) Let us consider:  58x = 182t + 130 Substitute the value of t = 0, 1, 2, 3, .…

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: 2x² + 3x = 14(mod19) X = * (mod19)

A: Given,            2x2+3x≡14 (mod 19).