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5

Part of 2010 Dutch BxMO TST

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permutation is quadratic if k+a_k is square, existence for every n

Source: Dutch BxMO TST 2010 p5

8/24/2019
For any non-negative integer nn, we say that a permutation (a0,a1,...,an)(a_0,a_1,...,a_n) of {0,1,...,n}\{0,1,..., n\} is quadratic if k+akk + a_k is a square for k=0,1,...,nk = 0, 1,...,n. Show that for any non-negative integer nn, there exists a quadratic permutation of {0,1,...,n}\{0,1,..., n\}.
permutationQuadraticnumber theoryPerfect Square