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

Q: . If 9x = 15 (mod 37), then x mod 37 is 14 17 33 11

A:

Q: All final answers must be in Zn where n is the mod 5) + 45 mod 18 2 mod 13 1 11 = 1

A: We have to find the values of x according to the given information

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

A:

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: If a≡b (mod m) and c ≡d (mod m),show that (b) ac≡bd (mod m).

A: Given : a≡b (mod m) c ≡d (mod m), We have to show  ac≡bd (mod m)

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: 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: 2. Prove directly if the statements that are true, give counterexamples to disprove those that are…

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 27 mod 7. Then x is 54 55 None of the option 46

A:

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

A:

Q: 7. Calculate each of the following. [from #22, 4.5] b) 971321 (mod 765) a) 2557341 (mod 5681)

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: He have to Show that lon = (-1)" (mod 1") shall use mathematical moluction Let Pin) := lon a (47"…

A:

Q: 3. Show that ifn = 2 (mod 4), then 9" + 8" is divisible by 5.

A: Here we will prove the given statement.

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

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 a = b (mod m) and a = b (mod n), and gcd (m,n) = 1, then a = b (mod mn) Select one: O True O…

A:

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

A:

Q: If x = 2 (mod 5) and y = 4 (mod 5) then 2x – 3y =? (mod 5)

A:

Q: 8, Suppose a,b € Z. Prove that a = (mod 5). b (mod 10) if and only if a = b (mod 2) and a = b

A:

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

A:

Q: 4. Using your work from the earlier parts or independently find: (a) mod 8 (b) + mod 23 17 (c) mod 7

A: Given

Q: If n| m and a = b(mod m), then a = b(mod n).

A:

Q: 9. Show that if p is an odd prime and p = 3 mod 4 then p is not the sum of the squares of two…

A: In the given question we have to prove that if p is an odd prime and…

Q: Prove the following results. (I). If n = 2(mod 4), then n is the sum of three squares of integers.…

A:

Q: 11. If an+1 = 2an + 3 and ao = 1, then az = %3D 509 O 513 O 487 O 496

A:

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

A:

Q: Let S := {1< a<p - 1: () = 1} . Ifp = 1 mod 4, show that Σ p(p – 1) 4 rES

A:

Q: 8. Compute the following. (a) (17 mod 6) (b) (256 mod 31) (c) (-2245 mod 7)

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Q: If a+c=b+c (mod m) then a =b (mod m) Select one: True False

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: If 5x = 12 (mod 41), then the value of x (mod 41) is O 33 O 19 D 27 O 17

A:

Q: Prove that if a = b mod n and c= d mod n, then ac bd mod n.

A: Given if a≡bmodn and c≡dmodn We have to show that ac≡bdmodn. Now, a≡bmodn…

Q: If a = b (mod 5), then... Choose all correct statements. O a3 = b³ (mod 5) O a + b = 0 (mod 10) O a…

A: Option (a), (c), and (d) are correct options.

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

A:

Q: 5. Let C = {x ∈ Z|x ≡ 7( mod 9)} and D = {x ∈ Z|x ≡ 1( mod 3)}. (a) If C ⊆ D? Justify your…

A:

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 a # 0 (mod m) and b # 0 (mod m), then ab# 0 (mod m). Select one: O True False

A: justification is given in step 2)

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: 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: 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).

Q: Let S:= {1<a<p – 1:() = 1} . Ifp = 1 mod 4, show that p(p – 1) 4 rES

A:

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.