H Home Tools34★LO56Acrobat Reader File Edit View Sign Window HelpO)Additional Practic... xDiscrete Mathema...Additional Practice Problems on Proof.pdf11. If m is an even integer and n is an odd integer, then mn-m is divisible by 4.OCT10/ 12. Suppose a is a natural number > 1. Prove that if a|(b+15) and a|(b+22), then_a=7.2803. Suppose m is a natural number. Prove that if m² – 9 is prime, then_m= 4.4. For all positive real numbers a and b, if a< b then a ‹ b³ . You may assume that the product of twopositive numbers is positive, and the product of two negative numbers is also positive.479D5. We know that if gcd(a, b) = 1, then there exist integer solutions to the equation ax+by= 1. Prove thefollowing more general statement: Let gcd(a, b) = d. If dc, then there exist integer solutions to theequation_ax+ by= c. (Hint: as a starting point, consider the integers a/d and b/d. In particular, what istheir gcd?)StvLAO2fPdelodAddMon Oct 10 3:47 PMSearch 'Crop Page'Export PDFAdobe Export PDFConvert PDF Files to Wordor Excel OnlineSelect PDF FileAdditional ...n Proof.pdfConvert toOMicrosoft Word (*.docx)Document Language:English (U.S.) ChangeConvertEdit PDFCreate PDFSign InCommentCombine FilesW^XV

●●● H Home Tools 3 1999 Additional Practic... x Discrete Mathema... Additional Practice Problems on Proof.pdf 1 /1 @ Eu 1. If m is an even integer and n is an odd integer, then mn-m is divisible by 4. 2. Suppose a is a natural number> 1. Prove that if a (b+15) and a (b+ 22), then a = 7. 3. Suppose m is a natural number. Prove that if m² -9 is prime, then m = 4. OCT 10 4. For all positive real numbers a and b, if a< b then a

●●● H Home Tools 3 1999 Additional Practic... x Discrete Mathema... Additional Practice Problems on Proof.pdf 1 /1 @ Eu 1. If m is an even integer and n is an odd integer, then mn-m is divisible by 4. 2. Suppose a is a natural number> 1. Prove that if a (b+15) and a (b+ 22), then a = 7. 3. Suppose m is a natural number. Prove that if m² -9 is prime, then m = 4. OCT 10 4. For all positive real numbers a and b, if a< b then a

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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17. Evaluation of proofs See the instructions for Exercise (19) on page 100 from Section 3.1. (a) For each natural number n with n > 2, 2" > 1 +n. Proof. We let k be a natural number and assume that 2k > 1 + k. Multiplying both sides of this inequality by 2, we see that 2k+1 > 2+ 2k. However, 2 + 2k > 2 + k and, hence, 2k+1 > 1+ (k + 1). By mathematical induction, we conclude that 2" >1+ n.