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Part of 1949 Miklós Schweitzer

Problems(1)

Miklos Schweitzer 1949_3

Source:

10/2/2008
Let p p be an odd prime number and a1,a2,...,ap a_1,a_2,...,a_p and b1,b2,...,bp b_1,b_2,...,b_p two arbitrary permutations of the numbers 1,2,...,p 1,2,...,p . Show that the least positive residues modulo p p of the numbers a1b1,a2b2,...,apbp a_1b_1, a_2b_2,...,a_pb_p never form a permutation of the numbers 1,2,...,p 1,2,...,p.
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