MathDB

20

Part of 2001 Baltic Way

Problems(1)

Obtaining sequences through set steps of (a,b,c,d)

Source: Baltic Way 2001

11/17/2010
From a sequence of integers (a,b,c,d)(a, b, c, d) each of the sequences (c, d, a, b),  (b, a, d, c),  (a + nc, b + nd, c, d),  (a + nb, b, c + nd, d) for arbitrary integer nn can be obtained by one step. Is it possible to obtain (3,4,5,7)(3, 4, 5, 7) from (1,2,3,4)(1, 2, 3, 4) through a sequence of such steps?
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