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Home » So, \( 5^2 + 12^2 = c^2 \). - AMAZONAWS

So, \( 5^2 + 12^2 = c^2 \). - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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\sum_{k=1}^{10} k^3 = \left(rac{10 \cdot 11}{2}
ight)^2 = (55)^2 = 3025.
Now compute $3025 \mod 9$. Use the digit sum method:
Digit sum of $3025$: $3 + 0 + 2 + 5 = 10$, then $1 + 0 = 1$, so $3025...
Alternatively, divide: $3025 \div 9 = 336 imes 9 = 3024$, remainder $...
Thus, the remainder is $1$.
Therefore, the answer is $oxed{1}$.
Question: What is the greatest common divisor of $3^{15} - 1$ and $3^9...
Solution: Use the property:
\gcd(a^m - 1, a^n - 1) = a^{\gcd(m,n)} - 1, \quad ext{for } a > 1.

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