Divisible by 2 but Not 4

★ 7/10number theory Modular Arithmetic sequences Telescoping

Problem

Let $a_n = 1 + 2 + \cdots + n$ and $S_m = a_1 + a_2 + \cdots + a_m$ . Among $S_1, S_2, \dots, S_{2017}$ , how many are divisible by $2$ but not by $4$ ?

Answer

Solution

Difficulty	7/10
Topics	number theory, Modular Arithmetic, sequences, Telescoping

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