The integer n = 12700140x3243243 is missing the digit x. a) If n congruent to  3 (mod 9), then what is x ? Hint: Use the fact that 10 congruent to 1 (mod 9). b) If n congruent to 3 (mod 11), then what is x ? Hint: Use the fact that 10 congruent to –1 (mod 11).

Q: a) Prove that if p is prime and p  1≡ (mod 4), then ((p-1)/2)!)^2 ≡ -1 (mod p) b) Use part a) to…

A: According to the given information in part (a) it is required to prove that:

Q: 2. If x mod 5 = 4, then x could be O 571 O 400 O 633 O 719

A: Given               x(mod 5)=4

Q: Suppose b is any integer. If b mod 12 = 5, what is 6b mod 12? In other words, if division of b by 12…

A: Given b is an integer such that b mod12=5 To find the value of  6b mod12

Q: ct enumeration, find the period of the following congruential generator: Xi+1=11Xi mod 32, given…

A: Given, the congruential generator is :Xi+1 = 11Xi mod 32, Also, given X0 = 1 We see that the…

Q: Suppose b is any integer. If b mod 12 = 7, what is 8b mod 12? In other words, if division of b by 12…

A: Given b mod 12= 7  To find 8b mod 12

Q: Use the table in VII to give a formal proof of the following. For all integers a and b, if a = 1…

A:

Q: an is an even number, show that a2 = 0 (mod 4), and if an is an odd number, show that a2 = 1 (mod…

A:

Q: Find the value of 3443 mod 23 4 16 O 3

A:

Q: x is congruent to 43 mod 12. Then x is

A: x is congruent to 43 mod 12 implies x congruent 7 (mod 12). So, solution in the least residue system…

Q: x is congruent to 43 mod 12. Then x is None of the option 91 75 89

A: Answer is 91.

Q: For which odd primes p is 5 a square mod p?

A:

Q: 1. How many solutions( mod 419) does x = 186 mod 419 have? (Show your work!) 2. How many solutions (…

A: Given: x2≡186 mod 101 We need to solve x2≡186 mod 101 and how many solution exists.

Q: 2. Determine x >0 for each case: 5903 = x (mod 60), 17342 =r (mod 5).

A:

Q: What is the closest prime p following 123456 that satisfies p=3 (mod 4)

A:

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

A:

Q: The value of 9446 (mod 47) is: 46 O 47

A: 9446(mod 47)

Q: a. Let m be an integer such that m mod 5 = 2, what is 8m mod 5? b. Let n be an integer such that n…

A: Consider the given information: Let m be an integer such that m mod5 = 2. Then m=5k+2   where…

Q: What is the value of o(5400 mod 13)

A: From Fermat's Theorem we know that if p is a prime number and p/a, a∈Z  then ap-1≡1(mod p) Since,…

Q: The prime number 8191 is a None Mersenne prime number Carmichael number Inverse of 7 modulo 11

A: Given that The prime number 8191 is

Q: 2

A:

Q: Let P be a prime, if ac = bc (mod p) and p does not divide c, then a = b (mod p) Select one: O True…

A: Given  gcd(c, p) = 1 and ac ≡ bc(mod p). (We may assume p > 1 so that c  ≠  0.) Then ac − bc =…

Q: x is congruent to 43 mod 12. Then x is None of the option 89 91 75

A:

Q: 9 The residue of 6 (mod 5) is (Round to the nearest whole number.)

A:

Q: Is it true that 90 ≡ 64 (mod 13)?

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

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

A:

Q: #5. Suppose that a = 2 (mod 113), and b = 5 (mod 113) What is (a b + 56b + 155) mod 113?

A: given a≡2(mod113),b=5(mod113)a3≡23(mod113)a3b≡235(mod113)56b≡280(mod113)56b≡54(mod113)155≡15mod113)

Q: The value of 538 mod 11 is O 10 O 8

A:

Q: 122 is congruent to 5 modulo17 ?

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

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

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

Q: Show that if p and q are distinct primes, then pª-1 + q®=1 = 1 (mod pq).

A: Given problem is to show the following identity using congruence, we have to consider that…

Q: determine what number the sum is congruent to in mod 3, 6+4 = __ (mod 3)

A: First we add the numbers, then check for the remainder on dividing the result by 3 and that will be…

Q: In the formula a b (mod n), what is the value of b in 36 b (mod 5)?

A:

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

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

Q: (b) Prove that if a = 7 mod 10 and b = 6 mod 15, then a + b = 3 mod 5.

A: Our objective is to prove . Since you have posted multiple questions I am solving one.

Q: The equation 82x = 12 (mod 13) has O 1 incongruent solution modulo 12 O 4 incongruent solutions…

A: First Option Is Correct Answer.

Q: Suppose b is any integer. If b mod 12 = 7, what is 6b mod 12? In other words, if division of b by 12…

A: To determine the value of 6b mod(12) if b mod(12) = 7.

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: Prove that if n is an odd integer, then n^2 is congruent to 1 modulo 8.

A:

Q: Find a two digit integer c such that 101c = 1 mod 107. This congruence has a unique solution mod 101…

A: We need to find a digit integer c such that 101c ≡ 1 mod 107. As per the given question, this…

Q: Show that : If n is an integer then n is congruent to 0 modulo 4 or 1 modulo 4.

A:

Q: In the congruence equation 3x + 12 = mod 10, which of the following is FALSE O a. 5, 15, 25, 35,..…

A:

Q: mod 32, given Xo=1 Please answer w

A: The congruential generator is given as:Xi+1 = 11Xi mod 32, where we are given X0 = 1. We see that,…

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

A:

Q: If a (mod 0) = a, How would you interpret the congruence a ≡ b (mod 0)?

A: According to the given information, it is given that:

Q: Which is the solution of 71x congruent to 5 mod 142. 38 57 85 None of the above

A: To determine which of the given is the solution of 71x≡5mod142.

Q: If a = 2846463 mod 59, then a =? A

A:

Q: Find all solutions mod 31 to the congruence x° = -5 (mod 31).

A:

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

A:

Q: For which primes p > 7 is 7 a square mod p? Your answer should be of the form p = {a1, a2,... , a}…

A: Given: p>7 ,If 7 is a square mod p.

Q: For any integers m and n, if m mod 11 is 6 and n mod 11 is 7, what is m+n mod 11? 13 9 42

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.