Why do Christmas and New Year's Day always fall on the same day of the week? O 25 ( mod 7) = 31 ( mod 7) O 7( mod 25) = 31 ( mod 7) 7( mod 25) = 7( mod 31) O 7( mod 7) = 31 ( mod 25)

Q: Any number n is congruent to the sum of its digits modulo 4. Select one: True False

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Q: 4. Find all numbers between -50 and 50 which x mod 13 = 3

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Q: (a) Show that if n 7 mod 8, then n + 6n 3 mod 8.

A: If, n = 7 (mod 8) So, n² = 7² (mod 8) So, n² = 49 (mod 8) So, n² = 1 (mod 8)

Q: Suppose a and b are integers, a = 15 (mod 23), andb=7 (mod 23). Then integer c with Osc< 22 such…

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Q: 2= 12 mod 2 - - 2 = 11 mod 18 20 = -2 mod 19 - 2= 20 mod 2 - -17 = 20 mod 8 6.7 = -14 mod 11 - -1 =…

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Q: For which primes p > 5 is -5 a square mod p? Your answer should be of the formp = {a1, a2, ..., ak}…

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Q: He have to Show that lon = (-1)" (mod 1") shall use mathematical moluction Let Pin) := lon a (47"…

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

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Q: Which expression is equivalent to [77 · (-65) + 147] mod 7? O 7 O [(147 mod 7) · (-65 mod 7) + (77…

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Q: If n is an integer and 3n + 2 is even then n is even. (You may use any kind of proof)

A: Given: To prove that if n is an integer and 3n+2 is even then n is even.

Q: What prime numbers are squares in mod 17? (Include primes that are larger than 17). What primes p…

A: Since the squares less than 17 are 1, 4, 9, 16 then the prime numbers that are squares in mod 17 are…

Q: 4. If x mod 7 = 3, then x27 mod 7 is O 3 0 6 O 5 O 4

A: Given :- x mod 7 = 3

Q: If 19 7 (mod 6) and 27 =3 (mod 6) then 19x27 =7+3 (mod 6) 19+27 7-3 (mod 6) 19+27 7x 3 (mod 6) 19+27…

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Q: Suppose that message is to be encrypted using the formula c=9p mod 26. What is the formula that you…

A: The message p is encrypted as c using the formula, c≡9p (mod 26)

Q: 2n3 + 3n2 +n ≡ 1 (mod 6) Select one: True False

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Q: True or False?  −29≡5(mod 17)

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Q: Find  mod (40, 7) and div (40, 7).   mod(40, 7)=? div(40, 7)=?

A: 1) mod(40,7)  is the remainder when 40 is divided by 7we know that 7×5 =35  and 7×6=42as 7×6=42 is…

Q: Is it true that 90 ≡ 64 (mod 13)?

A: As given equation 90≅64(mod 13) is False.

Q: solve for x^2 = 1 mod 8 and x^2 = 1 mod 10

A: Solution...

Q: where _13-4 mod 13

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Q: I have a message 2,3,6,5 (mod.7),  I will find a check digit by multiplying the first and third…

A: Here, First number= 2 Second number =3 Third number= 6 Fourth number= 5

Q: 122 is congruent to 5 modulo17 ?

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

Q: The inverse of 3 modulo 7is -2

A: Given statement, The inverse of 3 modulo 7 is -2.

Q: Find the smallest positive integer for which x mod 3=2 and x mod 4=3   What is the next smallest…

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Q: Is 17 congruent to 4 modulo 6.

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

Q: (-130 mod 20·265 mod 20) mod 20 ?   clear answer please

A: a mod b gives the remainder when a is divided by b That is we express it as a=b q+ r where r is the…

Q: Which of the following are true modulo 12? (1) Does 5z = 6 mod 12 have a solution? How many? (2)…

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Q: Find  mod (59, 10) and div (59, 10).

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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: 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: (4) Let p be a prime number. Then r = 1 mod p has exactly two solutions modulo p.

A: 4) To prove, x2≡1mod p has exactly 2 roots such that p is a prime number.

Q: What is the result of: 6(40 – 13) (mod 11) The result is 8

A: Given 6(40-13)(mod 11)

Q: If 3x = 6 mod 9, when -2 <x< 8. Then O x=(-1, 3, 5} x=(-1, 2, 5} O x=(-1, 2, 3} O x=(-1, 5, 6}

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Q: Suppose that a and b are integers, a ≡ 7 (mod 19), and b ≡ 5 (mod 19), Find the integer c with 0 ≤ c…

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Q: which one will give a solution of [6,13] a)4x is identical to 3 mod 7 b)9x is identical to 11 mod…

A: which one will give a solution of [6,13]

Q: 17° = 7° (mod 4)

A: 178≡78(mod 4) That is: 178-78=6969990640 is divisible by 4.

Q: If 3x = 6 mod 9, when -2 < x< 8. Then O x={-1, 3, 5} x-1, 2, 5} O x=(-1, 2, 3} O x=(-1, 5, 6}

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Q: Find all integers X satisfying X ≡ 1 mod 6, X ≡ 3 mod 8, X ≡ 7 mod 9

A: First divide 1 i.e. the dividend by 6 i.e. the divisor 1/6 = 0.16667 Then multiple the whole part of…

Q: 5^14 ( mod 26).

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

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Q: Find the whole number of (3+12) =7 mod 10

A: The given equation (3x+12) ≡7 mod 10. Consider the following congruence equation (3x+12) ≡7 mod 10.…

Q: Is 27 = 31 mod 5 true or false?

A: False

Q: Which are true for modulo 12? 1.) Does 5x ≡ 6 mod 12 have a solution? How many? 2.) Does 4x ≡ 6 mod…

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Q: Compute 22 mod 3, 24 mod 5, 26 mod 7.  What do you notice?  Does Fermat predict your answers? (If…

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Q: 8. a = 20 (mod 31) and -15 s as 15.

A: As per the guidelines I am supposed to answer the first question only . For the other questions…

Q: 2222 (mod 13) is equal to 12 (mod 13) 2 (mod 13) None of the mentioned 6 (mod 13) 1 (mod 13)

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Q: Find (173 mod 29)4 mod 19.

A: Find (173 mod 29)4 mod 19.

Q: What are the FOUR values of x that will satisfy: x=2 mod 4 & x=3 mod 6 please show your…

A: Given: x≡2 mod 4  &amp; x≡3 mod 6   x≡a(mod m1)x≡b(mod m2) has a solution if and only if…

Q: 12x ≡ 18 (mod 15) has exactly 3 distinct solutions modulo 15 Select one: True False

A: 12x ≡ 18 (mod 15) has exactly 3 distinct solutions modulo 15 Select one: True False