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Home » Counting all combinations for \((a, b)\): - Carbonext

Counting all combinations for \((a, b)\): - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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2Question: What is the remainder when $2025 + 2027 + 2029 + 2031$ is d...
Solution: First, compute the sum:
+ 2027 + 2029 + 2031 = (2025 + 2031) + (2027 + 2029) = 4056 + 4056 = 8...
Now divide $8112$ by $12$:
\div 12 = 676 ext{ exactly, since } 12 imes 676 = 8112.
Thus, the remainder is $0$.
Therefore, the remainder is $oxed{0}$.
Question: What is the largest possible value of $\gcd(a,b)$ if the sum...
Solution: Let $a + b = 2024$, and suppose $d = \gcd(a,b)$. Since $d \m...
Additionally, since both $a$ and $b$ are even, $d$ must be even (becau...

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