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Home » A_{\textsquare} = 4^2 = 16 - NBX Soluciones

A_{\textsquare} = 4^2 = 16 - NBX Soluciones

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 Thus, the number of distinct schedules is \(\boxed{150}\).Question: How many of the 100 smallest positive integers leave a remainder of 2 when divided by 5?

📌 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} $.

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