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OMK 2018 Bongsu, Section B Problem 2

Source: OMK 2018 Bongsu, Section B Problem 2

June 20, 2021

Proofnumber theorycontests

Problem Statement

Prove that the number

9^{(a_1 + a_2)(a_2 + a_3)(a_3 + a_4)...(a_{98} + a_{99})(a_{99} + a_1)}

−

1

is divisible by

10

, for any choice of positive integers

a_1, a_2, a_3, . . . , a_{99}

.

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