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straints: • The penny starts at the point (1, 1) •From any point (i, j), the penny can move to (2i, j) or (i, 2j) • From any point (i, j), the penny can move to (i-j,j) if i > j, or to (i, j - i) if j> i. For which positive integers x, y can the penny be moved to (x, y). The statement should be an "if and only if", hence two implications must be proved.

straints: • The penny starts at the point (1, 1) •From any point (i, j), the penny can move to (2i, j) or (i, 2j) • From any point (i, j), the penny can move to (i-j,j) if i > j, or to (i, j - i) if j> i. For which positive integers x, y can the penny be moved to (x, y). The statement should be an "if and only if", hence two implications must be proved.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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15. A penny is moved in the cartesian plane according to the straints: • The penny starts at the point (1, 1) • From any point (i, j), the penny can move to (2i, j) or (i, 2j) • From any point (i, j), the penny can move to (i-j, j) if i > j, or to (i, j - i) if j> i. For which positive integers x, y can the penny be moved to (x, y). The statement should be an "if and only if", hence two implications must be proved.
Transcribed Image Text:15. A penny is moved in the cartesian plane according to the straints: • The penny starts at the point (1, 1) • From any point (i, j), the penny can move to (2i, j) or (i, 2j) • From any point (i, j), the penny can move to (i-j, j) if i > j, or to (i, j - i) if j> i. For which positive integers x, y can the penny be moved to (x, y). The statement should be an "if and only if", hence two implications must be proved.
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