1. Prove or give a counterexample: If x is irrational, then is irrational 2. Prove or give a counterexample: There do not exist three consecutive even integers a, b, and c such that a2 + b2 = c2 3....

1. Prove or give a counterexample: If x is irrational, then

is irrational

2. Prove or give a counterexample: There do not exist three consecutive even integers a, b, and c such that a²
+ b²
= c²

3. Prove or give a counterexample: The sum of any five consecutive integers is divisible by five.

4. Prove or give a counterexample: The sum of any four consecutive integers is never divisible by four