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Problem 3: Proof by contradiction Prove the following: There are no rational number solutions to the equation x'+x+1=0, i.e. no solution can be written as a ratio a/b where a and b are integers (you can always consider a/b to be reduced to lowest terms). Problem 5: Proof by induction Prove by induction that a). E%=o(p) = 2n b). S(n)= i(n-1+1) - =1*n+2(n-1)+3(n-2)+ +(n-2)*3+(n-1)*2+n*1=(***)

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