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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