Let a, b be coprime integers. Prove that every integer x > ab- a- b can be written as na mb where n, m are non-negative integers. Prove that ab -a - b cannot be expressed in this form

Q: Abstract Algebra. Please explain everything in detail.

A: To prove (or disprove)  the possibilty of required representations under the given conditions

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A: Introduction: Even and odd numbers are also referred to as: Even Number: An even number is one that…

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A: we have 15a+20b =49 and a and b both are in R  we prove that a and b are not both integers.

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Q: Prove that multiplication is associative in Q.

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A: Given that,         α is an integer in Q-37 lets consider  α=-37⇒α-1=-37-1

Q: 4. Prove that if m and n are positive integers and x is a real number, then %3D m

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A: We have to use properties of union in this question.

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Q: Let A be a set of integers closed under subtraction. Prove that if A is nonempty, then 0 is in A.

A: Let A be a set of integers closed under subtraction. Prove that if A is nonempty, then 0 is in A.

Q: prove that if a and b are both odd integers, then ab+1 is an even integer

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Q: division of a2 with 4 is either 1 or 0.

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Q: Prove that if a, b and c are positive integers such that a divides b and b divides c, then a divides…

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