1. Prove: If n is an integer, then n 2 + n 3 is an even number. 2. Prove: If n is odd, then n 2 = 8k + 1 for some integer k. 3. Prove: There exists an integer n such that n 2 + 3n/2 = 1. Is this...

1. Prove: If n is an integer, then n²
+ n³
is an even number.

2. Prove: If n is odd, then n²
= 8k + 1 for some integer k.

3. Prove: There exists an integer n such that n²
+ 3n/2 = 1. Is this integer unique?

4. Prove: There exists a rational number x such that x²
+ 3x/2 = 1. Is this rational number unique?