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Home » $ x + 3 \equiv 0 \pmod7 $, $ \pmod8 $ → $ x \equiv -3 \pmod7 $, $ \pmod8 $ - AMAZONAWS

$ x + 3 \equiv 0 \pmod7 $, $ \pmod8 $ → $ x \equiv -3 \pmod7 $, $ \pmod8 $ - AMAZONAWS

📅 March 6, 2026 👤 scraface
Mar 06, 2026
$ x + 3 \equiv 0 \pmod{7} $, $ \pmod{8} $ → $ x \equiv -3 \pmod{7} $, $ \pmod{8} $

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📌 We use the stars and bars transformation: if we place 3 A’s with at least one non-A between them, we first reserve 2 non-A’s to enforce spacing. So, we place 3 A’s and use 2 of the 5 non-A’s as "separators" between them. That leaves $5 - 2 = 3$ non-A’s to distribute freely in the 4 possible gaps: before the first A, between A1 and A2, between A2 and A3, and after the third A.

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