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Let \(a, b \in \mathbb{Z}\). Show that if \(7 \mid 2 a + 3 b\), then \(7 \mid 5 a + 4 b\). Hint. Find a \(\mathbb{Z}\)-linear combination \(\lambda (2a + 3b) + 7 \mu\) that equals \(5 a + 4 b\).
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