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Home » \( \fraczx - z = \fracza + b \) - Nelissen Grade advocaten

\( \fraczx - z = \fracza + b \) - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Solution: We are looking for integers $ n $ such that $ n \equiv 2 \pmod{5} $ among the first 100 positive integers.

📌 The sequence of such numbers is $ 2, 7, 12, \dots, $ forming an arithmetic progression with first term 2 and common difference 5.

📌 Let the general term be $ a_k = 2 + (k - 1) \cdot 5 = 5k - 3 $.

📌 We want $ a_k \leq 100 $, so:

📌 5k - 3 \leq 100 \Rightarrow 5k \leq 103 \Rightarrow k \leq \frac{103}{5} = 20.6

📌 Thus, $ k = 1, 2, \dots, 20 $, so there are 20 such numbers.

📌 Therefore, the number of integers is $ \boxed{20} $.

📌 Question: What is the remainder when the sum $ 1^3 + 2^3 + 3^3 + \dots + 10^3 $ is divided by 7?

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