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a nice number theory problem from iran tst

Source: Iranian TST 2018, third exam day 1, problem 2

April 18, 2018
IranIranian TSTmaximum valuealgebra

Problem Statement

Find the maximum possible value of kk for which there exist distinct reals x1,x2,…,xkx_1,x_2,\ldots ,x_k greater than 11 such that for all 1≤i,j≤k1 \leq i, j \leq k, xi⌊xj⌋=xj⌊xi⌋.x_i^{\lfloor x_j \rfloor }= x_j^{\lfloor x_i\rfloor}.
Proposed by Morteza Saghafian
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