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Large a, b, c, d satisfying 1/a + 1/b + 1/c + 1/d = 1/(abcd)

Source: All-Russian Olympiad 2006 finals, problem 9.2

May 7, 2006

inductionnumber theory proposednumber theory

Problem Statement

Show that there exist four integers

a

b

c

d

whose absolute values are all

>1000000

and which satisfy

\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}=\frac{1}{abcd}