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Home » \[ 3n^2 + 2 = 425 \] - Veritas Home Health

\[ 3n^2 + 2 = 425 \] - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 We seek integers \( n \) such that \( n \equiv 3 \pmod{7} \). The sequence of such integers is \( 3, 10, 17, \ldots \).

📌 This is an arithmetic sequence with the first term \( a = 3 \) and common difference \( d = 7 \). The general term is given by:

📌 n_k = 3 + 7(k-1) = 7k - 4

📌 We require \( n_k \leq 50 \):

📌 7k - 4 \leq 50

📌 7k \leq 54

📌 k \leq \frac{54}{7} \approx 7.71

📌 Thus, \( k \) can be any integer from 1 to 7. Therefore, there are 7 integers in the first 50 that are congruent to 3 modulo 7. The answer is \(\boxed{7}\).

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