三、假設 p = 3k + 2 是一個質數。試證：如果 p 可整除多項式 \(a^2 + ab + b^2\)(a 和 b 都是整數) ，則 a 和 b 必定都是 p 的倍數。(15 分)

二、英文作文（35 分）As people nowadays travel or migrate more widely and frequently around the globe, the job of immigration officers especially at the airport has become more significant than ever. Problems that an immigration officer might encounter include incomplete travel documents, expired visas, unclear purposes of entry, the use of forged or altered documents, and inconsistent statements from travelers. When such cases happen, immigration officers should conduct further inspection and even arrange interviews with targeted travelers. The mastery of professional English communication skills has thus been a must for each officer. Discuss the importance of professional English communication for immigration officers working at international airports in 250 words. Please express your thought with illustrations or concrete examples.

三、假設 p = 3k + 2 是一個質數。試證：如果 p 可整除多項式 \(a^2 + ab + b^2\)(a 和 b 都是整數) ，則 a 和 b 必定都是 p 的倍數。(15 分)

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