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smallest k>6 such 1 + 2 +...+ k = k + (k+1) +...+ n for n>k

Source: Dutch NMO 2006 p3

September 21, 2019
SumminimumArithmetic Progressionalgebra

Problem Statement

1+2+3+4+5+6=6+7+81+2+3+4+5+6=6+7+8. What is the smallest number kk greater than 66 for which: 1+2+...+k=k+(k+1)+...+n1 + 2 +...+ k = k + (k+1) +...+ n, with nn an integer greater than kk ?
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