Find all natural number \(n\) such that \(n\), \(n^2 + 10\), \(n^2 - 2\), \(n^3 + 6\), \(n^5 + 36\) are all prime numbers.
2 years ago
Note to self: 1 is not a prime number.
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This is from the First HK TST.
One question from me:
Is every odd prime representable in form of 4k \( \pm\) 1, where k \( \epsilon \) N ? Or Is every prime greater than 3 is representable in form of 6k \( \pm\) 1, where k \( \epsilon \) N ?
Every odd number (not necessarily prime) is representable in the form \( 4k \pm 1 \) for a suitable k.
And for \( 6k \pm 1 \) ?
Yes every prime is representable in the form \(6k\pm 1\).
\(6k, 6k +2,6k+4\) are divisible by 2
\(6k+3\) is divisible by 3