29. How many different values are there for 4n(mod 7), as n ranges over all positive integers? 30. If your birthday is on a Monday this year and neither this year nor the next year is a leap year, what day of the week will your birthday be on next year?

Q: If m is an integer, and if (m mod 11) = 6, then what is (5m mod 11)? 2 4 11

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

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Q: 9. Let a and b be integers. Prove that if a =7 (mod 8) and b = 3 (mod 8), then: (a) a + b = 2 (mod…

A: Your questions solution below in images

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

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Q: Suppose b is any integer., If b mod 12 = 7, what is 4b mod 12? In other words, if division of b by…

A: Given : b mod 12 = 7

Q: Prove the statement by contradiction.

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Q: 5- If a = b mod(n), then ac = bc mod(n). 6- If a b mod (n), then ak = b*mod(n) for every positive…

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

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Q: 5- If a = b mod (n), then ac = bc mod (n). 6- If a = b mod(n), then ak = bkmod(n) for every positive…

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Q: Consider 3 · 1, 3 · 2, 3 · 3, . . . , 3 · 12 all mod 13, or in other words, the multiples of 3 in…

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Q: 15 Composite Then and O modn Show that if n there are with X#0 od n and y7 but where yy= Omod n.

A: Given n is a composite number

Q: 9. This question is a little more challenging. How many integers in the interval [1, 99 999] (i.e.,…

A: Given data:   The given sum of all digits is k=10. The number of digits that can be used is n=5.…

Q: Let n be an integer greater than 1. If (n-2)! ≡ 1 mod n, then Prove n is a prime number.

A: Use the Wilson theorem and different case to solve this problem as in next step.

Q: Prove: The nth Fibonacci number Fn is even if and only if 3 | n.

A: The nth Fibonacci number Fn is even if and only if 3|n.

Q: 1. How many positive integers of 5-digit-number can be formed from the prime numbers starting at 1…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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

A:

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

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

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Q: 22. Suppose c is an integer. If c mod 15 = 3, what is 10c mod 15? In other words, if division of c…

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Q: Suppose c is an integer. If c mod 15 = 3, what is 10c mod 15? In other words, if the division of c…

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Q: (b) Proposition. For each integer m, 5 divides (m-m). Proof. Let m e Z. We will prove that 5 divides…

A: We need to find the correct proof of the given proposition.

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: If a = 1 (mod n) and b = 1 (mod n) then a - b = 0 (mod n) اختر واحدا: 2 3

A: True.

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

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: If n is an integer, then (2n² + 3n)# 3(mod5).

A:

Q: he smallest positive integer x such that x = 22 (mod 25), x =

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Q: (c) For all integers a and b, if a · b = 1 (mod 6), then a =1 (mod 6) or b = 1 (mod 6). (d) For all…

A: (c) The statement is false. For example take a=5, b=5 ab=2525≡1 mod(6) Hence ab≡1 mod(6) But a≡5…

Q: mod n, then x ≡ 0 mod n or

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Q: The least residue of 5500 mod(17) is Select one: O none O 7 O 13 O10 O 8

A: The least residue is, 13 The detailed solution is as follows below :

Q: 3. Find the last two digits of the number 99°. [Hint: 9° = 9 (mod 10); hence, 99 = = 99+10k. notice…

A: In question number 3: we have to find the last two digits of the number (((9)^9)^9) That means to…

Q: Suppose b is any integer. If b mod 12 = 7, what is 5b mod 12? In other words, if division of b by 12…

A:

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: 23. Let a,be Z and n eN. If a =b (mod n), then a = ab (mod n). (24, If a b (mod n) and c=d (mod n),…

A:

Q: The order of 5 mod 17 is

A: “Since you have asked multiple question, we will solve the first question for you. If you  want any…

Q: 3. If x mod 4 = 1 and y mod 4 = 3, then xy could be O 901 O 299 O 508 O 113

A: We shall use the division algorithm

Q: (a) What is 84 (mod 9)? (b) What is 52 (mod 5)? (c) What is -4 (mod 10)?

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Q: For any integer n, either n2 mod 4 = 0, or n² mod 4 = 1.

A: For any integer n, we prove that either n2 mod4=0,  or n2 mod4=1

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: Prove or disprove: for any integers a, b, c, d, if a= c (mod n) and b= d (mod n), then ab = cd (mod…

A: Given: For any integers a, b, c, d if a≡cmod n and b≡dmod n To show: ab≡cd (mod n) To say that a is…

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: 12.ifa b(mod n) and b a c(mod n) then ab m be(mod n)

A: We can proove in the following way:-

Q: 20. If a e Z and a = 1 (mod 5), then a² = 1 (mod 5). If a - h (mod n) then a3 = h3 (mod n)

A: Notation: a|b  means a divides b or                   a|b means b is divisible by a.

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: