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Home » White & Fluffy? These Puppies Are the Fluffiest White Dogs You’ll Ever See! - Crosslake

White & Fluffy? These Puppies Are the Fluffiest White Dogs You’ll Ever See! - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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+ 1 + 3 + 5 = 16 \equiv 0 \pmod{8}
Question: What two-digit positive integer is one more than a multiple...
Solution: Let $ x $ be the two-digit number. We are given:
x \equiv 1 \pmod{7}, \quad x \equiv 3 \pmod{5}
We solve this system using the Chinese Remainder Theorem.
Let $ x = 7k + 1 $. Substitute into the second congruence:
7k + 1 \equiv 3 \pmod{5} \Rightarrow 7k \equiv 2 \pmod{5} \Rightarrow...
So $ k = 5m + 1 $, and $ x = 7(5m + 1) + 1 = 35m + 8 $.
We now find a two-digit value of $ x $:
35m + 8 \geq 10 \Rightarrow m \geq 0, \quad 35m + 8 \leq 99 \Rightarro...

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