Sum them:

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• \( a=0, b=1 \): 5
• \( a=1, b=1 \): 15
• \( a=2, b=1 \): 45
• + 3 + 9 + 5 + 15 + 45 = 78
• Thus, the sum of all odd divisors of 180 is \(\boxed{78}\).
• Question:** A philosopher of science reflects on the elegance of symmetry and periodicity, drawing parallels to number theoretic identities. What is the greatest common divisor of $2^{10} - 1$ and $2^{15} - 1$?

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