Past exam of the mathematics course of the University of Cambridge / 2004 / ia / Paper 4 / 1E / b / Solution

Divide the linear congruence by the common factor $3$, also dividing its modulus:The Bézout's identity from part (a) makes $19$ the inverse of $79$ modulo $100$. Multiplication by $19$ therefore gives $x\equiv 133\equiv 33(\mathrm{mod}100)$. Thus all integer solutions are $\boxed{x=33+100k,k\in \mathbb{Z}}$. Equivalently, the three solution classes modulo $300$ are $33,133,233$; using modulus $300$ must not discard two of these classes.