Paper 4, Section I, E

Use Euclid's algorithm to determine $d$, the greatest common divisor of 203 and 147 , and to express it in the form $203 x+147 y$ for integers $x, y$. Hence find all solutions in integers $x, y$ of the equation $203 x+147 y=d$.

How many integers $n$ are there with $1 \leqslant n \leqslant 2014$ and $21 n \equiv 25(\bmod 29) ?$

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