Prove directly from the definitions that for all integers the Same parity Divide Bnt 19. and E m and have n n ,then 5m + Zn is evern Cases: both and are m. both and and n both odd. even. m are

Q: Abstract Algebra. Answer in detail please.

A: To prove the statements about the given field extensions, (two quadratic and one 4th degree over Q)

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Q: contradiction

A: Please refer to the image below

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Q: let a, b, and m be integer, prove that if 2a+3b>=12m+1, than a>=3m+1, or b>=2m+1

A: To prove: For integer a, b, and m if   2a+3b≥12m+1Than, either a≥3m+1, or b≥2m+1.

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Q: 2. Prove that if m and n are integers and mn is even, then m is even or n is even.

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Q: b. H = {x E G|x" = e} for a fixed positive integer n.

A: Given set in part B

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Q: Prove that if m and n are integers and mn is even, then m is even or n is even.

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Q: let m, n exist in the integers. n does not equal 0. prove that if n2 x2 - 2mnx+m2 = n2, then x is…

A: x is a rational number proved directly.