Word Count : 355

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हम दिए गए बहुपदों के गुणा और जोड़ की गणना करेंगे, ध्यान रखते हुए कि गणनाएँ \(\mathbb{Z}_5\) और \(\mathbb{Z}_7\) में की जानी हैं। --- ### (i) जोड़: \[ (\overline{2}x^3+\overline{3}x^2+\overline{4}x+\overline{1})+(\overline{3}x^3+\overline{4}x^2+\overline{2}x+\overline{3}) \] चूँकि यह \(\mathbb{Z}_5[x]\) में है, हम प्रत्येक पद के गुणांक को 5 से मॉड लेंगे: - \(x^3\) के लिए: \(2 + 3 = 5 \equiv 0 \mod 5\) - \(x^2\) के लिए: \(3 + 4 = 7 \equiv 2 \mod 5\) _____ ______ _____ ___ ________ ______ _________.
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