東京大学 新領域創成科学研究科 海洋技術環境学専攻 2023年8月実施 第3問

Author

祭音Myyura

Description

素数 を⽤いて と表される素数をすべて求めよ。

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Find all the prime numbers represented by , where and are prime numbers.

Kai

If are odd primes, then and are both odd, so is even and .

Hence one of must be . Let the other be an odd prime . Then

For , note (since is odd) and , so .

For , , which is prime.

Also, gives , not prime.

Therefore, the only prime of the form with prime is