Exercise 1: Square-and-Multiply Trace for 5^9 mod 11 — Possible Solution
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GIVEN
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a = 5, b = 9, n = 11. 9 in binary is 1001.

STEP-BY-STEP TRACE
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Start: base = 5 mod 11 = 5, result = 1

Bit 1 (rightmost, value 1): bit is 1 -> result = 1*5 mod 11 = 5
  Square base: 5^2 mod 11 = 25 mod 11 = 3

Bit 2: bit is 0 -> no multiply
  Square base: 3^2 mod 11 = 9 mod 11 = 9

Bit 3: bit is 0 -> no multiply
  Square base: 9^2 mod 11 = 81 mod 11 = 4

Bit 4 (leftmost, value 1): bit is 1 -> result = 5*4 mod 11 = 20 mod
  11 = 9
  Square base: 4^2 mod 11 = 16 mod 11 = 5 (this final squaring
  isn't used further since all 4 bits have now been processed)

RESULT
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5^9 mod 11 = 9

Total multiplications: 4 squarings + 2 bit-triggered multiplies
(at bit 1 and bit 4) = 6 multiplications total, dramatically fewer
than the naive approach's 9.

WHY THIS WORKS AS AN ANSWER
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Every one of the 4 bits of 9 (1001 in binary) is processed in
order, with squaring happening every iteration and the extra
multiply happening only when the corresponding bit is 1, matching
this chapter's own algorithm exactly - and the final answer matches
what Python's own pow(5,9,11) computes.