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📅 May 5, 2026 👤 scraface

May 05, 2026

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$ 7 $: prime
$ 8 = 2^3 $, $ 9 = 3^2 $ → coprime to others
So $ \text{lcm} = 7 \cdot 8 \cdot 9 = 504 $, correct.
Hence, no two-digit number satisfies $ x \equiv -3 \pmod{504} $.
The smallest positive solution is $ x = 501 $, which is three-digit.
Therefore, there is **no two-digit** such number.
But perhaps the question meant **three less than a multiple of 7, or 8...
Alternatively, maybe it meant a number such that $ x + 3 $ is divisibl...
Thus, no solution exists in two digits.
But for olympiad style, perhaps the intended setup was different. Let’...

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