In the congruence equation 3x + 12 = mod 10, which of the following is FALSE O a. 5, 15, 25, 35,.. are the solutions. O b. Original solutions can be found by substituting the variable with natural number values less than the modulus (mod 10) for which the congruence is true. O C. 15 is a solution. O d. Additional solutions can be obtained by adding the modulus (mod 10) to the original solution

Q: The integer n = 12700140x3243243 is missing the digit x. a) If n congruent to  3 (mod 9), then what…

A: According to the given information, Consider the given integer n:

Q: Give the following system (M). x = 2(mod 13) x = 1(mod 14) x = 3(mod 15) x = 2(mod 16) Which among…

A:

Q: TRUE or FALSE: 1. If a is congruent to b (mod m), then a^k is congruent to bk (mod m) for every…

A:

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

A:

Q: Christians who use the the Revised Common Lectionary have their daily liturgies alternate between…

A:

Q: Give an odd prime p congruent to ±1 modulo 12. Show that (3) = 1.

A: Please see the attachment

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

A:

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

A: Answer is 91.

Q: x is congruent to 27 mod 7. Then x is 54 55 None of the option 46

A:

Q: Where would 129 be on a mod 13 clock (which goes from 0 to 12)? What is the remainder…

A: Where  would  129  be  on  a  mod  13  clock  (which  goes  from 0 to 12)? What is the remainder…

Q: x is congruent to 31 mod 6. Then x is 40 54 55 None of the option

A:

Q: a) How can an inverse of a modulo m be used to solve the congruence ax ≡ b (mod m) when gcd(a,m) =…

A:

Q: 1. Find the value for q given: (a) 39 = 4( mod 5) (b) -43 = 1( mod 4)

A: Note: Hi! Thank you the question, As per the honor code, we'll answer the first question since the…

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

A:

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: Find all solutions to the following quadratic congruences by first making the leading coefficient 1…

A: Topic:- algebra

Q: Identify if the given statement is true or false: I. If a is an integer, the (a^2 is congruent to 0…

A: Given some statements. Check whether these statements are true or false.

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

A:

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

A:

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

A: We will use python code to find the solutions Now x5 ≡  -5 (mod 31)  ≡  26  (mod 31) And we only…

Q: (b) By applying part (a), solve the congruences 2x = 1 (mod 31), 6x = 5 (mod 11) 3x = 17 (mod 29).…

A:

Q: Find the solutions of the congruence 15x2 + 19x ≡ 5 (mod 65)

A: The given equation is: 15x2+19x≡5(mod 65)

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

A:

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)?

A:

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

A:

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: 2. Find all solutions, or show there are none, to the congruence X78 = 5 (mod 19)

A: By Fermat little theorem x18≡1mod19. Therefore, x4×18+6≡x6mod19 or x78≡x6mod19.

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

A:

Q: Find all solutions to the simultaneous congruences x = 4 mod 315 x = 9 mod 715 Give your answer as a…

A: The given simultaneous congruences are:…

Q: -) Find the solutions, if any, of each congruence. 21x 10 (mod 35) 9x = 15 (mod 21).

A: We know that, ax≡b mod n has solution if and only if gcd(a,n) divides b.

Q: 24. Given the linear congruence (16x is congruent to 72 mod 24.) How many possible incongruent…

A: 24. To find the number of incongruent solutions of16x≡72mod 24

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: 1. The product of (5254)^143 and (14344)^143 under modulo 143 is congruent to ___. a. 98 b. 121 c.…

A: To find: 1) The product of 5254143 and 14344143 under modulo 143 is congruent to ________.…

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: Which of the following is not a possible value for y ≡≡ 17 mod 8 in the equation ? Group of answer…

A: Consider the given equation.

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: If a = 3 (mod12) then a does not equal 1 (mod6)

A: a=b mod n if and only if n divides a-b Now, we have that a=3mod 12 We need to show that a≠1mod 6 Let…

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

A:

Q: Find all solutions to the congruence 10x≡5 mod 15 (b) Prove that 7 divides 32n+1+ 2n+2for any…

A: In  (a) we use the extended Euclidean algorithm to solve the problem. In (b) we use the mathematical…

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: solution to the congruence equation (3x + 12) = 7 mod 10

A: Given :  3x+12=7mod 10⇒     3x=7-12 mod 10⇒     3x=-5 mod 10⇒     3x=5 mod 10        -5 mod 10 =5⇒…

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

A:

Q: The equation 21x = 49 (mod 77) has: O no solution modulo 77 only 11 non-congruent solutions modulo…

A: Here we have given equation,  21x = 49 (mod 77)    Let a, b and m be integers such that m&gt;0 and…

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: The equation 12x=24 (mod 48) has: O 24 non-congruent solutions modulo 48 6 non-congruent solutions…

A: To find- The number of solutions for the given equation.

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&gt;7 ,If 7 is a square mod p.