# Question: problem 1 prove that n is an odd integer if...

###### Question details

Problem 1. Prove that n is an odd integer if and only if there is an integer m such that n = 2m + 7.

Problem 2. Let a be an integer. Prove by contradiction that a and a+4 cannot both be divisible by 3.

Problem 3.

1. Let a be an integer. Prove that 2|a if and only if 2|a^3.

2. Prove that 2^(1/3) is irrational.