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Home » Question:** How many of the 150 smallest positive integers are congruent to 3 (mod 7)? - Appcentric

Question:** How many of the 150 smallest positive integers are congruent to 3 (mod 7)? - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 But since we are to express the population as a power of 3, note that 324 = \( 3^4 \times 4 = 81 \times 4 = 2^2 \cdot 3^4 \). So:

📌 \text{Population} = 2^2 \cdot 3^4 \cdot 2^{t/3} = 2^{2 + t/3} \cdot 3^4

📌 For the population to be at least \( 3^k \), we need:

📌 3^4 \cdot 2^{2 + t/3} \geq 3^k \implies 2^{2 + t/3} \geq 3^{k - 4}

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