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Omni-MATH / Is it possible to find 100 positive integers not exceeding 25,000, such that all pairwise sums of them are different?

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problem

Is it possible to find 100100 positive integers not exceeding 25,00025,000, such that all pairwise sums of them are different?
Plain-text mathematical notation (without MathML)
Is it possible to find  100 positive integers not exceeding 25,000, such that all pairwise sums of them are different?
Original LaTeX notation
Is it possible to find  $100$ positive integers not exceeding $25,000$, such that all pairwise sums of them are different?

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