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Home » Experts Say This Is When Apple Cider Vinegar Starts to Spoil—Spoiler: It’s Sooner Than You Think! - AMAZONAWS

Experts Say This Is When Apple Cider Vinegar Starts to Spoil—Spoiler: It’s Sooner Than You Think! - AMAZONAWS

Experts Say This Is When Apple Cider Vinegar Starts to Spoil—Spoiler: It’s Sooner Than You Think!

📅 March 6, 2026 👤 scraface
Mar 06, 2026
Experts Say This Is When Apple Cider Vinegar Starts to Spoil—Spoiler: It’s Sooner Than You Think!

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📌 Multiplying both sides by the modular inverse of 4 modulo 7, which is 2 (since $4 \cdot 2 = 8 \equiv 1 \pmod{7}$), we get:
📌 So $k = 7m + 2$. Then $x = 60k = 60(7m + 2) = 420m + 120$. We seek the smallest three-digit such $x$:
📌 But what about $3 \cdot 5 = 15$? We saw $120$ in previous problem, but here product $1 \cdot 3 \cdot 5 \cdot 7 = 105$, divisible by $15$, but $3 \cdot 5 = 15$ — yes. But $3 \cdot 3 = 9$: $105$ not divisible by $9$. So $9$ does not always divide $P$.

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