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increasing sequence , a_n = 2023

Source: 2023 South Russian Girls MO - Assara Juniors p7

February 28, 2024
algebraSequence

Problem Statement

Given an increasing sequence of different natural numbers a1<a2<a3<...<ana_1 < a_2 < a_3 < ... < a_n such that for any two distinct numbers in this sequence their sum is not divisible by 1010. It is known that an=2023a_n = 2023. a) Can nn be greater than 800800? b) What is the largest possible value of nn? c) For the value nn found in question b), find the number of such sequences with an=2023a_n = 2023.
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