Let x, y be integers, and n be a natural number. Prove that x ^(2n) −...

Let x, y be integers, and n be a natural number. Prove that x ^(2n) − y ^(2n) is divisible by x + y

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Colby Messinger answered 2 years ago

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Let the cardinal number of N, the set of all natural numbers, be א0. Prove that...

Let the cardinal number of N, the set of all natural numbers, be א0. Prove that the product set N × N = {(m,n);m ∈ N,n ∈ N} has the same cardinal number. Further prove that Q+, the set of all positive rational numbers, has the cardinal number N_0. Hint: You may use the formula 2^(m−1)(2n − 1) to define a function from N × N to N, see the third example on page 214 of the textbook.

Prove these scenarios by mathematical induction: (1) Prove n2 < 2n for all integers n>4 (2)...

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Let x, y be integers, and n be a natural number. Prove that x ^(2n) −...

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