Solved: a. Use proof by contradiction to show that for any
Chapter 4, Problem 4.277(choose chapter or problem)
a. Use proof by contradiction to show that for any integer n, it is impossible for n to equal both 3q1 +r1 and 3q2 +r2, whereq1,q2,r1, andr2, are integers, 0r1 < 3,0r2 < 3, and r1 =r2. b. Use proof by contradiction, the quotient-remainder theorem, division into cases, and the result of part (a) toprovethatforallintegersn,ifn2 isdivisibleby3then n is divisible by 3. c. Prove that3 is irrational.
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