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

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

A:

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

A: To explain why Christmas and new year's day always fall on the same day of the week.

Q: Prove that if ca = cb (mod n), then a = b (mod n/d) , where d = gcd(c,n). %3D

A:

Q: If a= b (mod n) and gcd (a, n) = d, then gcd (b, n) = d :Select one True False

A:

Q: Determine 51 mod 13, 342 mod 85, 62 mod 15, 10 mod 15, (82  73)mod 7, (51 + 68) mod 7, (35 . 24) mod…

A:

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: II. Give FIVE different answers for each of the following. 1. 49 = mod 10 2. 82 = mod 9 3. 100 = mod…

A: 1) Given expression is  49≡______ mod 10

Q: mod

A:

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

A:

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

A: Given that 419 mod 7

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

A: Answer is 91.

Q: If x1 mod 17 = 5 then %3D x mod 17 = 7 x mod 17 = 6 Ox mod 17 = 5

A:

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

A:

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…

A:

Q: The inverse of 7 modulo 26 is 15

A: Given a statement

Q: and (mod 18), calculate (17)(49°. (496 –76+1) (mod 19)

A:

Q: Question 13 3 = 5 (mod2) OTrue O False

A: We have to check that the given statement is true or false.

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

A:

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

A: 9446(mod 47)

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: 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: Let n ∈ Z. Prove that if n^2 + 2n −4 doesnt equal 1 (mod 5), then 5 doesnt divide n.

A:

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: Given these statements about a, b, and c, • a = 3 (mod 8) • b = 2 (mod 8) • c = 1 (mod 6) Which of…

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: If a ≡ b(mod n) and c ≡ d(mod n), then ac ≡ bd(mod n)

A:

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

A:

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: The last two digits of 52044 is 44. If ab = 0 (mod 3), then a = 0 (mod 3) or b = 0 (mod 3). F 10. F…

A:

Q: 12 765,986 = 6 (mod 10) Select one: O True O False

A:

Q: 25. The value of x in (7x is congruent to 12 mod 17) is O 16 15 9 13 (mod 17)

A:

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

A:

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

A:

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

A:

Q: which one of the following is a congruence ? O 39 = 5 mod 5 O 23 = 4 mod 5 O 29 = 5 mod 15 O 48 = 8…

A:

Q: 5. The value of 693 mod 11 is O 3 O 7 O 6 4

A:

Q: The gcd of 7544 and 115 is: O 23 O 15 O 3

A:

Q: If a = b (mod 5), then... Choose all correct statements. O 2(a – b) = 0 (mod 20) O a³ = b3 (mod 5) O…

A:

Q: 27 = x(mod 5) is true if x =

A:

Q: Choose all statements that are correct. O 24 = 23 (mod 6) O 15 # 51 (mod 6) 32 = 16 (mod 8) O 71 =…

A:

Q: I. Determine whether each of these integers are congruent to 3 mod 7. 1. 37 2. -17 3. 86

A: We will find out the required solution.

Q: 4. Find x in ASTU. * 17 15 O 2 O 8 O v32 O V514

A:

Q: Show that af +...+ a, = a1 + ...+ ap(mod p).

A:

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)?

A:

Q: 1. The value of (1.000) 27 is O 327 O 0.327 O 1.000 O Non of them

A: Any finite power of 1 gives you 1.

Q: If ab = 0 (mod m), then either a = 0 (mod m) or D=0 (mod m). Select one: O True False

A:

Q: If 3(26!) = x(mod29), then x = None of the choices O 11 13 15

A: The given problem is to solve the given congruence equation. 3(26!)= x (mod 29).

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.