Use the method of proof by cases to prove the following statement n3,n23n+3isodd 1.51 Let nZ0. If nmod4{2,3}, then n is not a perfect square. 4.52 Let n and m be integers. If nm is not evenly divisible by 3 , then neither n nor m is evenly divisible by 3 . (In fact, the converse is true too, but you don' have to prove it.) Prove that the following claims hold for all integers n0, by induction on n : 5.1i=0ni2=6n(n+1)(2n+1)