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a/c = b/d = *ab + 1)/(cd + 1) - All-Russian MO 2003 Regional (R4) 8.6

Source:

September 17, 2024

algebra

Problem Statement

For some natural numbers

a, b, c

and

d

the following equations holds:

\frac{a}{c}= \frac{b}{d}= \frac{ab + 1}{cd + 1} .

Prove that

a = c

and

b = d