HMMT November

Algebra Difficulty 4.8 AIME Find the answer

Find the next two smallest juicy numbers after 6, and show a decomposition of 1 into unit fractions for each of these numbers.

Your answer

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

Solution

12 and 15: $1=\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{12}$ , $1=\frac{1}{2}+\frac{1}{3}+\frac{1}{10}+\frac{1}{15}$ .

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