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5

Part of 2015 NZMOC Camp Selection Problems

Problems(1)

sums a_i + a_j form consecutive terms of an arithmetic progression

Source: New Zealand NZMOC Camp Selection Problems 2015 p5

9/19/2021
Let nn be a positive integer greater than or equal to 66, and suppose that a1,a2,...,ana_1, a_2, ...,a_n are real numbers such that the sums ai+aja_i + a_j for 1≤i<j≤n1 \le i<j\le n, taken in some order, form consecutive terms of an arithmetic progression AA, A+dA + d, ...... ,A+(k−1)dA + (k-1)d, where k=n(n−1)/2k = n(n-1)/2. What are the possible values of dd?
algebraArithmetic Progressionarithmetic sequence