Exercise 1: Bezout Coefficients for GCD(99, 78) — Possible Solution
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GIVEN
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a = 99, b = 78

STEP-BY-STEP TRACE (tracking q, r, s, t)
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q=1: r=78, s=0,  t=1
q=3: r=21, s=1,  t=-1
q=1: r=15, s=-3, t=4
q=2: r=6,  s=4,  t=-5
q=2: r=3,  s=-11, t=14

The remainder reaches 3, and the next division (r=6 divided by
r=3) would give remainder 0, so the algorithm stops with gcd=3.

RESULT
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gcd(99, 78) = 3
x = -11, y = 14

CHECK: 99*(-11) + 78*14 = -1089 + 1092 = 3

This matches the GCD found, confirming Bezout's identity holds for
this specific x and y.

WHY THIS WORKS AS AN ANSWER
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Every step's q, r, s, t values are shown explicitly following this
chapter's own tracking method, and the final x, y pair is verified
directly against the actual GCD rather than simply asserted to be
correct.