I was doing some exercises from the book called Basica Mathematics - Serge Lang and here's the two problems: 1) Prove that there is no positive rational number a such that a^2 = 3. You may assume that a positive integer can be written in one of the forms 3k, 3k + 1, 3k + 2 for some integer k.
2) Prove that if the square of a positive integer is divisible by 3, then so is the integer. Then use a similar proof as for the square root of 2.
Basically I was trying to do this problems but I normally guide with the answers to see on how to approach this problems. If anybody has any idea on how to do this I would appreciate it