Competition problem — Number theory

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Number theory Difficulty 5.3 AIME, harder Find the answer

1. Find the simple continued fractions of
a) $\sqrt{7}$
d) $\sqrt{47}$
b) $\sqrt{11}$
e) $\sqrt{59}$
c) $\sqrt{23}$
f) $\sqrt{94}$ .

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

1. a) $[2 ; \overline{1,1,1,4}]$
b) $[3 ; \overline{3,6}]$
c) $[4 ; \overline{1,3,1,8}]$
d) $[6 ; \overline{1,5,1,12}]$

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.