Test 1 Solution - MAS 4214/001 Elementary Number Theory...

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MAS 4214/001 Elementary Number Theory, Fall 2013TEST IName:Date: 09/25/2013(2 points)Time allowed: 50 minutesShowALLsteps. Fifty points equal 100%.Question 1.(8 points)True or false: Explanation is not needed. Assume thata,b,c,s,t,nare integers.(a) IfSis a nonempty set of integers, thenScontains a least element.(b) Ifxis a real number satisfyingx1<nx, thenx=n.(c) Ifas+bt= 1, then gcd(a,b) = 1.(d) Ifas+bt= 7, then gcd(a,b) = 7.(e) Assume thatanegationslash= 0. Ifd|a, thend≤ |a|.(f) gcd(a+bc,b) = gcd(a,b).(g) If 0|n, thenn= 0.(h) Ifa|bc, thena|bora|c.Answer:(a)F(b)T(c)T(d)F(e)T(f)T(g)T(h)FQuestion 2.(5 points)Find a closed form forproducttextnj=11 +1j.j=j+1j. Thennproductdisplayj=1parenleftBigparenrightBig
Keeping Scores:QuestionBonus123456TotalScoreOut of28515101011611

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