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a_ia_j+a_ka_l all equal

Source: IV Caucasus Mathematic Olympiad

April 7, 2019
algebra

Problem Statement

Vasya has a numeric expression □⋅□+□⋅□ \Box \cdot \Box +\Box \cdot \Box and 4 cards with numbers that can be put on 4 free places in the expression. Vasya tried to put cards in all possible ways and all the time obtained the same value as a result. Prove that equal numbers are written on three of his cards.
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