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Romanian National Olympiad 2024 - Grade 9 - Problem 2

Source: Romanian National Olympiad 2024 - Grade 9 - Problem 2

April 6, 2024

algebrafractional part

Problem Statement

Let

a

and

b

be two numbers in the interval

(0,1)

such that

a

is rational and

\{na\} \ge \{nb\},

for every nonnegative integer

n.

Prove that

a=b.

(Note:

\{x\}

is the fractional part of

x.

)