Number Theory Course 1. Let ? and ? be integers. Show that if ? + ?...

Number Theory Course

1. Let ? and ? be integers. Show that if ? + ? is odd, then ? and ? are of the opposite parity:
a. By giving a proof by contradiction

2. Let n be a natural number. Prove that (?+ 1)2 −1 is even if and only if n is even. You may use any suitable proof technique.

3. Using a proof by induction, show that 5 | 6? − 1, for all natural numbers ? .

Expert Solution

Colby Messinger answered 5 months ago

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