Question: Please help me answer this discrete problem. heres the question. Only answer about 1.2 . Photo solutions would be appreciate. explanatio. thank u Exercise 1.1

Please help me answer this discrete problem. heres the question. Only answer about 1.2 . Photo solutions would be appreciate. explanatio. thank u

Exercise 1.1 Euclid begins with two unequal numbers AB, CD, and continually subtracts the smaller in turn from the greater. Let's examine how this method proceeds "in turn" when subtraction yields a new number that is smaller than the one subtracted. Begin with AB = 162 and

CD = 31.

  • a.How many times must CD be subtracted from AB until a remainder is left that is less than CD? Let this remainder be denoted as IA.
  • b.Write AB = BI + IA numerically using the given value for AB and the computed value for IA.
  • c.How many times must IA be subtracted from CD until a remainder is left that is less than IA? Let this remainder be denoted as GC.
  • d.Write CD = DG + GC numerically using the given value for CD and the computed value for
  • e.How many times must GC be subtracted from IA until a remainder is left that is less than GC? Let this remainder be denoted as HA.
  • f.Is HA a unit?

Exercise 1.2. Apply the procedure outlined in Proposition 1 to the numbers AB = 625 and

CD = 288. Begin by answering questions (a)-(f) above except with the new values for AB and

CD.

(g) In this example, how should the algorithm proceed until a remainder is reached that is a unit?

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