a. Use proof by contradiction to show that for any integer n, it is impossible for n to eq...

a. Use proof by contradiction to show that for any integer n, it is impossible for n to equal both 3q1 + r1 and 3q2+ r2, where q1, q2, r1, and r2, are integers, 0 ≤ r1<3, 0 ≤ r2<3, and r1 ≠ r2.

b. Use proof by contradiction, the quotient-remainder theorem, division into cases, and the result of part (a) to prove that for all integers n, if n2 is divisible by 3 then n is divisible by 3.

c. Prove that  is irrational.