Let a and b be non relatively prime positive integers. If there exist integers s and t with as+bt=5 then * None of these a and b are relatively prime O gcd(a,b)=2 O gcd(a,b)=10 gcd(a,b)=5

Q: show that for all integers x and y (x-y)3=x3-y3(mod3)

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Q: 8. Let m 2q + 1 be an odd positive integer. Prove that every integer = is congruent modulo m to a…

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Q: 4. a) The function h(x) has a domain of (x = R}, while the function j(x) has a domain of {x = R |…

A: hx=x∈ℝjx=x∈ℝ|x>4 and x≠8h-jx=x∈ℝ|x≤4 and x=8     Hence the domain of h-jx is h-jx=x∈ℝ|x≤4 and x=8…

Q: Let a and b be integers with GCD(a, b) = d and let a = da', b = db'. Prove that GCD(a', b')=1

A: and  be integer such that .It is given that  and .We have to prove .Note: According to the…

Q: Let a be an integer greater than 0 and b be an integer greater than or equal to 0. Let a be greater…

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Q: Given a positive integer n, let a2,n–1 a2,n a3,n-2 a3,n-1 a3,n An = аn-1,2 аn-1,n-2 аn-1,п-1 @n-1,п…

A: Given: Here the given positive integer n, Let An = 00...00a1,n00...0a2,…

Q: find the amount of odd three-digit numbers that can be created. (

A: here given digits are  [0, 1, 2, 3, 4, 5, 6]. so there are total 7 digits . here use counting…

Q: [a, b] = N=1 (a -,b+-) To prove this, show the following: То Show that [a, b](a – ÷,b +- ) for every…

A: Given that, [a,b]=∩n=1∞a-1n,b+1n This can be written as, ∩n=1∞a-1n,b+1n=[a-1,b] The aim is to show…

Q: Prove that for all integers m>0 , m^2+5m+4 is composite.

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Q: Prove that If a is an element of order n and p is prime to n, then a\power{p} is also of order n.

A: is prime to We have to show

Q: Let m 2q be an even positive integer. Prove that every integer is congruent modulo m to a unique…

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Q: Prae that x4 -5x +3 is ineducible ouer Q

A: Given polynomial is f(x)= x^4 -5x^3 +3

Q: Let n and k be integers such that (n, k) = 1. Prove that (n, n − k) = 1.

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Q: {m belongs to all integers| m^2=3}    Now list the elements in the set?

A: The given set is {m belongs to all integers| m2=3}.To list down the elements in the given…

Q: Find the final amount of money in an account if $7, 600 is deposited at 6.5% interest compounded…

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Q: Prove that among 7 positive integers, there are always two integers such that either their sun or…

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Q: Let A = 1 = {n+ (−1)n 2" | REN}. n Compute sup A and inf A if they exist.

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Q: prove that for all integers m>2,m^2+m-6 is composite

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Q: Let n be an element in Z. Prove that 5|n^2 if and only if 5|n.

A: If n be an element in Z. We have to prove that 5|n^2 if and only if 5|n.

Q: Let n be a positive integer. Suppose that there are three pegs and on one of them n rings are…

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Q: Let a and b be relatively prime positive integers. Show that a(b) + b(a) = 1(mod ab).

A: Solution:

Q: Find the final amount of money in an account if $8,100 is deposited at 6.5% interest compounded…

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Q: Let a and b be integers with GCD(a, b) = d and let a = da', b = db'. Prove that GCD(a', b')=1

A: according to guidelines we can do only first question thank youLet a and b be integers with GCD(a,…

Q: Suppose n1,n2 are positive integers and gcd(n1,n2) = 1. Then for every integer x, if n1 | x and n2 |…

A: Given that gcd(n1,n2)=1 Then there exist integers m1 and m2 such that          m1n1+m2n2=1 Then…

Q: Prove that a1 + a2 = b₁ + b₂ mod n.

A: We have to prove that a1+a2=b1+b2 (mod n).Given:a1≡b1 (mod n)a2≡b2 (mod n)This means there exist…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.