22. Suppose c is an integer. If c mod 15 = 3, what is 10c mod 15? In other words, if division of c by 15 gives a remainder of 3, what is the remainder when 10c is divided %3D by 15?

Q: In your head, determine (2.1075 + 2)100 mod 3 and (10100 +1)99 mod 3.

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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: 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: If x mod 5 = 2 and y mod 5 = 3, then xy could be D 306 D 843 D 342 O 197

A: See solution below

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 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: (c) For each integer a, if a 4 (mod 8), then a 2 (mod 8).

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

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Q: (Adapted from Richardson problem 4.2.2, Solve the congruence 589.r = 494 (mod 817). Hint: The…

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Q: 1. The value of 419 mod 7 is O 5 0 6 O 3

A: Given that 419 mod 7

Q: The inverse of 7 modulo 26 is 15

A: Given a statement

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: If 9x = 15 (mod 37), then x mod 37 is %3D 33 11 14 O 17

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Q: Given a = 4( mod 9) and b = 5( mod 9), find c with 0<c<9 such that c = 5a + 3b ( mod 9)

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Q: 2. Suppose a, b, c, d are integers and that (a, b) = (c,d) = 1. If (g) + (á) show that b = ±d. is an…

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Q: The remainder in 14 (mod 3) is 3

A: Given that 14 (mod3)

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: The value of 52003 mod 7 is? 80 3) 4

A:

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

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Q: The value of 52003 mod 7 is? (3 (4 8) 9

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Q: i need to find the value of m 12 = (m*28)mod 113

A: Solution is given by using Diophantine equation and extended Euclidean algorithm as follows

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: Does x2 + 5x congruent to 12 (mod 31) have a solution? (Hint: complete the square)

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Q: d) If 72 = 1 (mod 5), with 0<r <4, then z =. e) The number of (positive) divisors of 23345 is

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Q: 1. Solve the congruence 17x ≡ 42 (mod 100). 2.Compute the remainder of 3293 when divided by 97…

A: 1) solve the congruence 17x=42+100k implies17≡42+100k as we know gcd17,100=1 and 1/42 now, using…

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

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Q: (18) If a, be Z, then (a + b)3 = a3 + b3 (mod 3).

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Q: 15 16 17 18 The number of integers between 15 and 100 that end with 4 or 6 is QUESTION 5 2 3 The…

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Q: Assume that the sum of the digits of a number, n, in base 10, equals to 16. Example: n= 97 is one…

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Q: State as TRUE or FALSE. d) 143 = -40 (mod 5) e) –4 = 788 (mod 3)

A: a≡b(mod n) means a-b is divisible by n

Q: Suppose that a = 3 mod 12 and b =7 mod 12 IfC = 3 a – 2 b mod 12 then C =

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Q: The value of 52003 mod 7 is? (3 4 8

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Q: Ha = b (mod n) and gcd (a,n)= d, then gcd (b,n) %3D

A: Given a≡b(mod n). This can be written as a-b≡0(mod n). Implies a-b=kn for some natural number k.…

Q: Consider the equation 2x + 1 = 0 mod n. For which n are there no solutions? one solution? multiple…

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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: 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: The order of 5 mod 17 is *

A: Since ϕ(17) = 16 Therefore order can be the divisor of 16 So the order can be 1,2,4,8 or 16

Q: b. 3x = 0 (mod 21)

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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: 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: b) 100 hours aft 24. Which decimal digits occur as the final digit of a fourth power of an integer?…

A: We have to find decimal digits occur as the final digit of a fourth power of an integer.

Q: x is congruent to 21 mod 8. Then x is None of the option 29 16 24

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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: Suppose a, b, c and d are integers. Prove that  if a divides b and c divides d, then ac divides bd

A: According to the given information:   It is given that a divides b, there is an integer x such that…

Q: Does

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Q: Suppose a # b (mod m). Let r be the remainder of a when divided by , and let s be the remainder of…

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Q: Calculate (13, 000 +2)10 (mod 13). Find the omeir lor of 3456 whon dlivided by the following Hint:…

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