MathDB
Modular arithmetic at mod n

Source: 2021 Turkey JBMO TST P6

May 24, 2021
number theorymodular arithmeticnumber theory proposed

Problem Statement

Integers a1,a2,…ana_1, a_2, \dots a_n are different at mod n\text{mod n}. If a1,a2−a1,a3−a2,…an−an−1a_1, a_2-a_1, a_3-a_2, \dots a_n-a_{n-1} are also different at mod n\text{mod n}, we call the ordered nn-tuple (a1,a2,…an)(a_1, a_2, \dots a_n) lucky. For which positive integers nn, one can find a lucky nn-tuple?
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