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5050 | a_k +a_l -a_m -a_n when 0 < a_1 < a_2 <... < a_{101} < 5050

Source: Switzerland - Swiss TST 2003 p9

February 18, 2020
number theorycombinatoricsdivides

Problem Statement

Given integers 0<a1<a2<...<a101<50500 < a_1 < a_2 <... < a_{101} < 5050, prove that one can always choose for different numbers ak,al,am,ana_k,a_l,a_m,a_n such that 5050∣ak+al−am−an5050 | a_k +a_l -a_m -a_n
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