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Minimizing sum given product!

Source: RMO Maharashtra and Goa 2016, P1

October 11, 2016
inequalitiesnumber theoryconstruction

Problem Statement

Find distinct positive integers n1<n2<⋯<n7n_1<n_2<\dots<n_7 with the least possible sum, such that their product n1×n2×⋯×n7n_1 \times n_2 \times \dots \times n_7 is divisible by 20162016.
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