Modular Arithmetic

(See attached file for full problem description) --- Seeking a clear path because do not understand this concept of modular arthimentic.

Collection of subsets for equivalence relations

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Discrete Mathematics

I would like to get a more detailed understanding of my homework. I am not looking for just answers, but more a step-by-step solution. I would like to know how? Prove the given statement: 1) The sum of an integer and it's square is even. 2) The sum of the squares of two odd integers cannot be a perfect square. 3) The sum of any three consecutive integers is even. 4) The product of two rational numbers is rational. 5) The product of two irrational numbers is irrational. 6) Prove that the cube root of 2 is not a rational number. 7) Prove that the square root of 3 is not a rational number. 8) If n is an even prime number, then n=2. 9) If n is an even integer, 4... click for more

Big O and Catalan number proof

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Undirected & Spanning Trees and Reverse Polish Notation

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