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Home » Master Stillness: How the Full Serenity Prayer Opens Doors to Total Tranquility - jntua results

Master Stillness: How the Full Serenity Prayer Opens Doors to Total Tranquility - jntua results

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 5Frage: Wie viele der 100 kleinsten positiven ganzen Zahlen sind kongruent zu 3 (mod 7)?

📌 Lösung: Um herauszufinden, wie viele der 100 kleinsten positiven ganzen Zahlen kongruent zu 3 modulo 7 sind, identifizieren wir zuerst die Zahlen, die diese Bedingung erfüllen. Eine Zahl \( n \) ist kongruent zu 3 modulo 7, wenn sie als \( n = 7k + 3 \) für eine ganze Zahl \( k \) geschrieben werden kann.

📌 Die kleinste positive ganze Zahl, die dies erfüllt, ist \( 3 \) (wenn \( k = 0 \)), und die Folge setzt sich fort als \( 3, 10, 17, 24, \ldots \). Dies ist eine arithmetische Folge mit dem ersten Glied \( a = 3 \) und der gemeinsamen Differenz \( d = 7 \).

📌 Wir müssen das größte \( k \) finden, sodass \( 7k + 3 \leq 100 \):

📌 7k + 3 \leq 100 \\

📌 7k \leq 97 \\

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