EECS 1019 Study Guide - Midterm Guide: Natural Number, Bijection, Asteroid Family

• School: York University
• Department: Electrical Engineering and Computer Science
• Course: EECS 1019
• Professor: Suprakash Datta

Document Summary

Math/eecs 1019 third test (version 2) fall 2014. Solutions: (3 points) if x is an integer and 7 divides 3x + 2, prove that 7 also divides 15x2 11x 14. Hint: consider the di erent cases for p mod 3 i. e. the remainder obtained after dividing p by 3. As the hint suggests, we can do a proof by cases. Note that p cannot be 3 (we know 3,5,7 are primes). Clearly p mod 3 cannot be zero if it is p is a multiple of 3 and not 3 so p cannot be prime. In this case, (p + 2) mod 3 = 0, i. e. , p + 2 is a multiple of 3 and thus not prime. In this case, (p + 4) mod 3 = 0, i. e. , p + 4 is a multiple of 3 and thus not prime.