HINTS FOR CWORK3: --------- Essay Revise the material on periodic continued fractions. There are many results, but most of them are technical lemmas, with only few main theorems. Identify those, and try to explain them in words: they are going to form the skeleton of the essay. Make sure you do not write too much, losing yourself in details. --------- Problem 1. First put each surd in standard form: (sqrt(D)+P)/Q. a) by simplifying b) by expanding, and then simplifying c) by summing the series Then use the formula given in the notes. --------- Problem 5. (a) Construct x_{m+1} and y_{m+1} from x_m and y_m, using surds and the concept of fundamental solution. Then equate rational and irrational parts. (b) Use part (a) twice, with m replaced by m+1 and m-1, respectively. --------- Problem 6. (c) Use part (b) and Thm 1.3.