MathDB

1

Part of 2007 Korea Junior Math Olympiad

Problems(1)

a_ix_i + x_{i+2 }\equiv 0 (mod 5) where a_i sequence, x_i \in N sequence

Source: KJMO 2007 p1

5/2/2019
A sequence a1,a2,...,a2007a_1,a_2,...,a_{2007} where ai∈{2,3}a_i \in\{2,3\} for i=1,2,...,2007i = 1,2,...,2007 and an integer sequence x1,x2,...,x2007x_1,x_2,...,x_{2007} satis fies the following: aixi+xi+2≡0a_ix_i + x_{i+2 }\equiv 0 (mod5mod 5) , where the indices are taken modulo 20072007. Prove that x1,x2,...,x2007x_1,x_2,...,x_{2007} are all multiples of 55.
number theorynumber theory with sequencesInteger sequenceSequencesmultiple