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Part of 2018 Dutch BxMO TST

Problems(1)

a_1, a_1a_2, a_1a_2a_3,..., a_1a_2a_3...a_p different remainders divided by p

Source: Dutch BxMO TST 2018 p3

8/24/2019
Let pp be a prime number. Prove that it is possible to choose a permutation a1,a2,...,apa_1, a_2,...,a_p of 1,2,...,p1,2,...,p such that the numbers a1,a1a2,a1a2a3,...,a1a2a3...apa_1, a_1a_2, a_1a_2a_3,..., a_1a_2a_3...a_p all have different remainder upon division by pp.
number theoryprime numbersDivisibility