MATH 2390 Midterm: MATH 2390 Kennesaw State Exam5solutions

• School: KSU
• Department: Mathematics
• Course: MATH 2390
• Professor: All

Document Summary

Remember that writing and correct use of notation are very important. Indicate here which of problems 1 10 you want me to grade:_________________________: prove that if x and y are both odd integers then 8| x2 y2 . Proof: since x and y are both odd then there exist integers r and s such that x 2r 1 and y 2s 1. This gives x2 y2 2r 1 2 2s 1 2. 4r2 4r 1 4s2 4s 1. 4 r2 s2 4 r s . 4 r s r s 4 r s . 4 r s r s 1 . At this point we can see that 4| r2 s2 . In addition we can see that if r s is even then. Thus, in order to complete the proof we only need to consider the case that r s is odd. Proof: since a b (mod n) then n| b a .