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Home » These Rare Amish Names Are Taking the Internet by Storm! - Carbonext

These Rare Amish Names Are Taking the Internet by Storm! - Carbonext

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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First, find the prime factorization of 60:
= 2^2 \times 3^1 \times 5^1
The divisors of 60 are of the form \( 2^a \cdot 3^b \cdot 5^c \) where...
To find the sum of even divisors, note that an even divisor must inclu...
\( a = 1 \) or \( a = 2 \)
\( b = 0 \) or \( b = 1 \)
\( c = 0 \) or \( c = 1 \)
We compute the sum:
\sum_{\substack{a=1\\b=0\\c=0}}^{2,1,1} 2^a \cdot 3^b \cdot 5^c
= \left( \sum_{a=1}^{2} 2^a \right) \cdot \left( \sum_{b=0}^{1} 3^b \r...

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We want where the expression is **less than 0**, so the solution is wh...
x \in (-\infty, 2) \cup \left(rac{11}{3}, \infty
oxed{(-\infty, 2) \cup \left(rac{11}{3}, \infty
Question: Let $ a, b, c $ be real numbers such that $ a + b + c = 0 $....
Solution: We use the well-known algebraic identity:
a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca).
Given that $ a + b + c = 0 $, substitute into the identity:
a^3 + b^3 + c^3 - 3abc = 0 \cdot (a^2 + b^2 + c^2 - ab - bc - ca) = 0.
a^3 + b^3 + c^3 = 3abc.
This completes the proof.

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