The least positive integer x satisfying 22010 = 3x (mod 5) is

Q: 16 M = 7 -5 Find formulas for the entries of M", where n is a positive integer. M" =

A: We have to find the entries of matrix Mn.

Q: let x  be a fixed but arbitrary integer. Do there exist infinity many integer y such that,…

A: Let x = x0 be fixed given integer. Then,

Q: Is it possible to raise a positive number b to a power and obtain a negative number? Is it possible…

A: The given statement is " The possibility to raise a positive number b to a power and obtain a…

Q: Find all solutions for x, up to congruence.  x ≡ 2^63 (mod 61).

A:

Q: find x, where x= 9753 (mod 120) and -120<x<0

A: Ans: -87

Q: find a Positive integern for which the equality holds %3D

A:

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

A:

Q: If x^677 ≡ 3 mod 2020, find x.

A: We have   x677≡3mod2020⇒x677-3=2020m   where m is integer different values of m we get different…

Q: Compute 2021^2021(mod 1000). The answer is 421. Show the work.

A:

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

A:

Q: What is the largest value that m mod n can be?

A: Largest value of m mod n is n-1.

Q: Solve the congruence 11x = 45 (mod 97) where x is an integer in the interval [0,97).

A:

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

A:

Q: Determine a positive integer x such that 57x +7 = 78 (mod53).

A:

Q: Find all solutions for x, up to congruence 7^78 (mod 79)

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Q: 3x = 11 (mod 20)

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Q: (d) (11 × 14" + 1) is a composite integer for every positive integer

A:

Q: Solve 65x ≡ 2(mod243) by inverse method

A: Given, 65x≡2mod 243 Here gcd65,243=1 Now find the inverse of 65 mod 243.…

Q: Solve x21 ≡ 6 mod 7

A: If p is a prime number then xp-1≡1(mod p) for all x∈ℤ~pk  where pk denotes multiples of p . Suppose…

Q: x² + x = 13(mod17) X= * (mod17)

A:

Q: Find a number a such that 70a = 1 mod 17.

A:

Q: Find the integer that satisfies: 30x4 ≡ 12 (mod 67)

A: Given the expression is, 30x4≡12mod 67

Q: 10.2 Find a number a that has the following three properties: (i) a = 73003 (mod 3750). (ii) 1 ≤ a ≤…

A:

Q: Find all integer values of x for which 3x = 4 (mod 8).

A: given congruence equation 3x≡4(mod 8)

Q: 17!=1(mod19). Select one: True False

A:

Q: there are 3 square roots of 0 when we work mod 45 give all 3 of them

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Q: Solve 10x = 13 (mod 53)

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Q: Give all non-negative solutions for 10r =-17 mod 4.

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Q: Solve 53x ≡ 31(mod85) in the form x ≡ b(modm), 0 < b < 85.

A: We will find out the required value.

Q: 4. A television producer is looking to release a new series. He believes that the hours per week…

A:

Q: 237 (mod 10)

A: We use the definition of a (mod b) to find the value of 237 (mod 10).

Q: prove the following using either direct or indirect proof  a. if a is an odd integer, then…

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Q: Derive the recursive formula using Newton-Raphson method for finding the reciprocal of a positive…

A:

Q: 5^14 ( mod 26).

A:

Q: Solve 529 = x (mod 11)

A: The given modulo equation is 529=xmod11. The modulo relation can be solved as: m≡kmod n if m-k is…