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Home » #### \(\frac{1 + \sqrt33}2\) - Aurero

#### \(\frac{1 + \sqrt33}2\) - Aurero

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 \gcd(6, 6) = 6

📌 Add 1 to include both endpoints:

📌 Therefore, the number of lattice points on the line segment is:

📌 What is the sum of all the even divisors of 60?

📌 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 \( 0 \leq a \leq 2 \), \( 0 \leq b \leq 1 \), \( 0 \leq c \leq 1 \).

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g(x) = ax^3 + bx^2 + cx + d
with conditions:
g(1) = a + b + c + d = 3 \quad \text{(1)} \\
g(2) = 8a + 4b + 2c + d = -1 \quad \text{(2)} \\
g(3) = 27a + 9b + 3c + d = 4 \quad \text{(3)} \\
g(4) = 64a + 16b + 4c + d = 10 \quad \text{(4)}
Now subtract (5) from (6):
Subtract (6) from (7):
Now subtract (8) from (9):
Substitute into (8):

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