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Home » Total number of ways to choose 3 distinct primes: - Abu Waleed Tea

Total number of ways to choose 3 distinct primes: - Abu Waleed Tea

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 So $ \text{lcm} = 8 \cdot 9 \cdot 7 = 504 $, yes.

📌 But 504 is large. So no two-digit number satisfies $ x \equiv -3 \pmod{504} $.

📌 Thus, **no solution**.

📌 But for olympiad creativity, perhaps the intended setup was:

📌 Find a two-digit number such that it is **three less than a multiple of 7**, **three less than a multiple of 8**, and **three less than a multiple of 9** — same as before.

📌 Alternatively, maybe the question meant:

📌 What two-digit positive integer is three less than a multiple of 7, and also three less than a multiple of 11?** But not.

📌 Perhaps the number is such that $ x \equiv -3 \pmod{7} $, $ x \equiv -3 \pmod{8} $, $ x \equiv -3 \pmod{9} $, same.

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