What is the remainder when 2021202120212021 is divided by 2020? use congruence modulo

Q: Find the answer of -16 mod 5

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Q: Find the least residue of 63^9 modulo 10

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Q: Any two integers are congruent modulo .when they are both even or both odd. Least common multiple…

A: Answer : smallest prime n=2

Q: Find the order of all element of Z8 under addition mod . Please brieflt explain and show all the…

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Q: Name all integers from -100 to 100 that are congruent to -1 modulo 25!

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Q: (a) Use cases based on congruence modulo 3 and properties of congruence to prove that for each…

A: (a) We will prove that  n3≡n(mod3) by the mathematical induction. For n=1 13≡1(mod3) ∴ it is true…

Q: primitive root modulo

A: Given: Value of n=223 in  mod n. To find: Primitive root modulo 223.

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

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Q: Compute the addition modulo operation 3+2 2 0. 1 3 O O

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Q: [Hint: Proceed by induction on n.] 16. Use the theory of congruences to verify that 89| 24 – 1 and…

A: The solution is given as follows :

Q: Two great mathematicians who have contributed greatly in the field of modular arithmetic are Swiss…

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Q: Show that every nonzero residue (mod 17) can be written as a power of 3

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Q: How many integers have inverses modulo 144? Justify.

A: Justify how many integers have inverse modulo 144.

Q: Find the inverse s of -1959 modulo 979 such that 0 <s< 979

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Q: How many elements are there in the greatest conjugacy class of 5 ?S

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Q: Determine what number the product is congruent to in mod 3. 5.8 5.8 = (mod 3 )

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Q: 5) Using Fermat's little theorem, determine 21998 mod 7. In other words, what is the remainder when…

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Q: Decide whether the following binomial congruence has any solutions x2" = 10 mod 103. Use modular…

A: We have to decide whether the following binomial congruence has any solutions or not.…

Q: What is 2 ^32 mod (5)?

A: mod is the function whose output is always positive. mod is represented by .

Q: 122 is congruent to 5 modulo17 ?

A: To check whether -122 is congruent to 5 modulo 17 or not

Q: Is 7|(15+20): True or False? 28 is congruent to 42 modulo 6: True or False?

A: I am solving these in step 2

Q: Determine how many ti (o bom is a prime.

A: In this question, the number of times is determined when 1 appears in the multiplication table for…

Q: Is 17 congruent to 4 modulo 6.

A: 17, when divided by 6, leaves remainder 5

Q: To Determine the value that 46 is congruent to IN modulo 7

A: Note that, If a and b are integers and n &gt; 0, then a ≡ b (mod n) to mean n|(b − a) and It can be…

Q: (a) Use cases based on congruence modulo 3 and properties of congruence to prove that for each…

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Q: whether 2 is a primitive root modulo 19. Please state the reason.

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Q: Any two integers are congruent modulo to: even integer odd integer Prime integer not a prime nor…

A: suppose n is a positive integer. Then two integers are said to be congruent modulo n if (a-b) is…

Q: Determine the remainder of 102020 modulo 2020 and the remainder of 102020 modulo 2021.

A: solution 104≡1920(mod2020)…

Q: Inverse of 9 modulo 23 is 18

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Q: 2. Find an inverse of 2 modulo 17 that is positive and less than 17.

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Q: The inverse of 19 modulo 141 is 51 صواب İhi

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Q: Find a number that is less than 1740719 which is congruent to 577 modulo 1279 and congruent to 317…

A: Given, a number that is less than 1740719 which is congruent to 577 modulo 1279 and congruent to 317…

Q: 29 is a primitive root modulo 38? True or False

A: The answer to this question is TRUE.

Q: . Find the value of 876,543,218,765,432,187,654,321 (mod 11) 10

A: To find the value of 876,543,218,765,432,187,654,321(mod11)

Q: Construct the addition and multiplication table for Z4 (Note that, both operations are mod4)

A: We have to solve given problem:

Q: Inverse of 19 modulo 141 is 141 193 192 192

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Q: Inverse of 9 modulo 23 is 18 17 - 18 -17

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Q: Determine whether 17 is congruent to 5 modulo 6?

A: We have to check whether 17 is congruent to 5 modulo 6

Q: Express 5^7 using base e

A: From the given information the given expression is:

Q: Two integers are congruent modulo to a)prime integer b)odd integer C) not a prime nor composite…

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Q: Inverse of 19 modulo 141 is

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Q: What is the modulus and argument of -3. Select all that apply

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Q: What is the largest n such that 16 and 25 are in the same remainder class modulo n? Write out the…

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Q: Find the order of 5 modulo 31.

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Q: Solve the congruence 200x = 13 (mod 1001). Give your answer as the smallest positive integer in its…

A: a = 200, m = 1001 Applying the Euclidean algorithm we get the inverse of 200 modulo 1001 is 996 (you…

Q: Inverse of 9 modulo 23 is 18 - 18 17 -17

A: We need find multiplicative inverse of 9 in z/23z

Q: true or false? explain this: 2 mod 5 ≡ 7 mod 5

A: a mod n  ≡ b mod n if n divides (a-b).