Let  J5 = {0, 1, 2, 3, 4},  and define  G: J5 ✕ J5 → J5 ✕ J5  as follows. For each  (a, b) ∈ J5 ✕ J5,   G(a, b) =   (3a + 1) mod 5, (4b − 1) mod 5

Q: Find the first three values of the linear congruential generator X; = 2x;–1 +3 (mod 13) starting…

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Q: Let a, b, x, y ∈Zbe such that ax+by= 11. May we conclude that gcd(a, b) = 11?Why or why not? (Write…

A: Consider the given information:Let a,b,x,y∈ℤ be such that ax+ by=11.

Q: Prove that A=I-N+N²-N³ for A & N definec as follows: N=A-I (identity), where |1 0 0 an & I= 0 1 0. 0…

A: given matrix  A=1a12a1301a23001 and I=100010001 prove  that A-1=I-N+N2-N3 where N=A-I

Q: (b) Let a.. and m be positive integers. Prove that if (a,m) = (b, m) = 1, then (ab, m) = 1.

A: Given  a, b and m are positive integers.  (a, m) = (b, m) = 1.We have to prove that (ab, m) = 1.

Q: Let a, b € N. Choose all correct statements. O gcd(-a, b) = gcd(a, -b) O ged(2a – b, a + b) =…

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Q: If a and b are even then GCD(a,b) must be 2

A: Given statement :- if a and b are even then GCD(a,b) must be 2

Q: Prove that π2 -1 is algebraic over Q(π3).

A: We have to prove that π2-1 is algebraic over Qπ3.

Q: Then, there exists k1≠0, k2≠0  such that a,b=k1c,k1d   and  c,d=k2e,k2f. a,b=k1c,d=k1k2e,…

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Q: Let V be all elements of R2 that have the form (a, a2) where a is a real number. Show that (3,9) is…

A: Let V be all elements of R2 that have the form (a, a2) where a is a real number. We have show that…

Q: Define g: ZX Z→ Z, g (x, y) = z, where z mod 3 = x and z div 3 = y. Find g (2, 2).

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Q: U(11) is cyclic generated by  Select one: a. 2 b. 10 c. 9 d. 5

A: Correct option a. 2

Q: Let A = [ L 1 -1 4 24 2 37 2 1 J , V = Is v in Nul(A)? Type "yes" or "no". no Is w in Nul(A)? Type…

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Q: Let a, b, c, d, e, and f be positive integers. Let d = gcd(a, b, c), e = gcd(a, b) and f = gcd(e,…

A: Given that for positive integers a,b,c,d,e,f , d=gcda,b,ce=gcda,bf=gcde,c

Q: Determine the value of k that satisfies the following identity (x is a variable). +k = In(x + ab?)…

A: Given equation is: lna+xb2+k=lnx+ab2 To evaluate value of k k=ln(x+ab2)-lna+xb2…

Q: find AB, BA, A +B, A - B, A, B, 5A, 3B. Observe that AB + BA. Show that (A - B)(A + B) # (A + B)(A –…

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Q: Evaluate the Boolean power A3 where [1 01 A = 1 1 1 1

A: Boolean Product : Let us consider two matrices A=[aij]m x n  and  B=bijn x p be zero-one matricies.…

Q: Find the solution to this recursive relation an = an−1 − n, a0 = 4

A: Question: Find the solution to the recursive relation an=an-1-n,   a0=4

Q: Let x € Z. Prove that if 2 | (x²-5) then 4 | (x²-5).

A: Given that .The objective, if then prove that .