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Solutions and Hints

C. D. Olds ,
Anneli Lax  and
Giuliana P. Davidoff
C. D. Olds
Affiliation:
San Jose University
Anneli Lax
Affiliation:
New York University
Giuliana P. Davidoff
Affiliation:
Mount Holyoke College
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Summary

Chapter 1

1 a. y = ⅔x + ⅕ (because 5 does not divide 3). Other examples are similar.

b. (because 3 | 15). (p0, q0) = (5, 1); {(pk, qk) = (5 + 15k, 1 + 2k), | k is any integer}.

2. Hint: Use the distance formula to find the length dk of the line segment from (pk-1, qk-1) to (pk, qk). If dk is not a function of k, then dk is constant from any point to any adjacent lattice point.

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The Geometry of Numbers , pp. 161 - 168
Publisher: Mathematical Association of America
Print publication year: 2000

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