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●●● 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 & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 36E
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H Home Tools 3 4 ★ LO 5 6 Acrobat Reader File Edit View Sign Window Help O) Additional Practic... x Discrete Mathema... Additional Practice Problems on Proof.pdf 1 1. If m is an even integer and n is an odd integer, then mn-m is divisible by 4. OCT 10 / 1 2. Suppose a is a natural number > 1. Prove that if a|(b+15) and a|(b+22), then_a=7. 280 3. 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 two positive numbers is positive, and the product of two negative numbers is also positive. 479 D 5. We know that if gcd(a, b) = 1, then there exist integer solutions to the equation ax+by= 1. Prove the following more general statement: Let gcd(a, b) = d. If dc, then there exist integer solutions to the equation_ax+ by= c. (Hint: as a starting point, consider the integers a/d and b/d. In particular, what is their gcd?) S tv LAO 2 f P delodAdd Mon Oct 10 3:47 PM Search 'Crop Page' Export PDF Adobe Export PDF Convert PDF Files to Word or Excel Online Select PDF File Additional ...n Proof.pdf Convert to O Microsoft Word (*.docx) Document Language: English (U.S.) Change Convert Edit PDF Create PDF Sign In Comment Combine Files W ^ X V
Transcribed Image Text:H Home Tools 3 4 ★ LO 5 6 Acrobat Reader File Edit View Sign Window Help O) Additional Practic... x Discrete Mathema... Additional Practice Problems on Proof.pdf 1 1. If m is an even integer and n is an odd integer, then mn-m is divisible by 4. OCT 10 / 1 2. Suppose a is a natural number > 1. Prove that if a|(b+15) and a|(b+22), then_a=7. 280 3. 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 two positive numbers is positive, and the product of two negative numbers is also positive. 479 D 5. We know that if gcd(a, b) = 1, then there exist integer solutions to the equation ax+by= 1. Prove the following more general statement: Let gcd(a, b) = d. If dc, then there exist integer solutions to the equation_ax+ by= c. (Hint: as a starting point, consider the integers a/d and b/d. In particular, what is their gcd?) S tv LAO 2 f P delodAdd Mon Oct 10 3:47 PM Search 'Crop Page' Export PDF Adobe Export PDF Convert PDF Files to Word or Excel Online Select PDF File Additional ...n Proof.pdf Convert to O Microsoft Word (*.docx) Document Language: English (U.S.) Change Convert Edit PDF Create PDF Sign In Comment Combine Files W ^ X V
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