Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 12"
(New page: ==Problem== {{empty}} ==Solution== {{solution}} ==See also== {{CYMO box|year=2006|l=Lyceum|num-b=11|num-a=13}}) |
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| − | ==Problem== | + | == Problem == |
| − | {{ | + | If <math>f(\alpha,\beta)= \begin{cases}\alpha & \textrm {if} \qquad \alpha=\beta \\ f(\alpha-\beta,\beta) & \textrm {if} \qquad \alpha>\beta \\ f(\beta-\alpha,\alpha) & \textrm {if} \qquad \alpha<\beta \end{cases} </math> |
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| + | then <math>f(28,17)</math> equals | ||
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| + | A. <math>8</math> | ||
| + | |||
| + | B. <math>0</math> | ||
| + | |||
| + | C. <math>11</math> | ||
| + | |||
| + | D. <math>5</math> | ||
| + | |||
| + | E. <math>1</math> | ||
==Solution== | ==Solution== | ||
| − | { | + | <math>f(28,17) = f(11,17) = f(6,11) = f(5,6) = f(1,5) = f(4,1) = f(3,1) = f(2,1) = f(1,1) = 1\ \mathrm{(E)}</math> |
==See also== | ==See also== | ||
{{CYMO box|year=2006|l=Lyceum|num-b=11|num-a=13}} | {{CYMO box|year=2006|l=Lyceum|num-b=11|num-a=13}} | ||
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| + | [[Category:Introductory Algebra Problems]] | ||
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