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m4thbl3nd3r   1
N Apr 15, 2025 by lbh_qys
With each $x\ne -2,-3$, define $f_1(x)=-\frac{3x+7}{x+2},f_2(x)=f_1(f_1(x))=-\frac{3f_1(x)+7}{f_1(x)+2},f_3(x)=f_1(f_2(x))=-\frac{3f_2(x)+7}{f_2(x)+2},\dots$ Find all integers $x$ such that $f_{269}(x)$ is an integer.
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m4thbl3nd3r
Apr 15, 2025
lbh_qys
Apr 15, 2025
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m4thbl3nd3r
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#1 h  Apr 15, 2025, 6:17 AM
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With each $x\ne -2,-3$, define $f_1(x)=-\frac{3x+7}{x+2},f_2(x)=f_1(f_1(x))=-\frac{3f_1(x)+7}{f_1(x)+2},f_3(x)=f_1(f_2(x))=-\frac{3f_2(x)+7}{f_2(x)+2},\dots$ Find all integers $x$ such that $f_{269}(x)$ is an integer.
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lbh_qys
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#2 h  Apr 15, 2025, 7:24 AM
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This post has been edited 1 time. Last edited by lbh_qys, Apr 15, 2025, 7:24 AM
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