Using congruences, solve the Diophantine equations below:
(a) 4x + 51y = 9.
[Hint: 4x ≡ 9 (mod 51) gives x: = 15 + 51t, whereas 51y ≡ 9 (mod 4) gives y = 3+4s. Find the relation between s and t.]
(b) 12x + 25 y = 331.
(c) 5x − 53y = 17.
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