Hi Everyone! I decided recently to start reading a book that acts as a transition to upper level mathematics. The last section of the chapter introduces you to the different proof techniques and mathematical facts to produce mathematical proofs. I think I understand everything, but I wanted to make sure by sharing my proof for a problem in the book. If anybody can chime in about if it is right or the like, please do so. 1. The problem statement, all variables and given/known data The product of two odd integers is odd. 2. Relevant equations N/A 3. The attempt at a solution Let m and n be two odd integers. We will prove that if m and n are odd integers, then the product of m and n is odd. Since m and n are odd, there exists two integers, i and j, that are an element of Z such that m=2i+1 and n=2j+1. Substituting (2i+1) and (2j+1) into m*n, we produce (2i+1)(2j+1) =>4ij+2j+2i+1 => 2(2ij+j+i)+1, where (2ij+j+1) is an integer. Since (2ij+j+1) is an integer, there exists an integer k that is an element of Z such that (2ij+j+1)=k. By substituting k for (2ij+j+1), we produce 2k+1, which is the definition of an odd number. Therefore, the product of two odd integers is odd.