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c >= 1 if (a + 1)/(b + c)= b/a , for a,b \in N, c>0

Source: 2021 Austrian Regional Competition For Advanced Students p1

May 31, 2021

inequalitiesalgebra

Problem Statement

Let

a

and

b

be positive integers and

c

be a positive real number satisfying

\frac{a + 1}{b + c}=\frac{b}{a}.

Prove that

c \ge 1

holds.
(Karl Czakler)