Waste less time on Facebook — follow Brilliant.
×

Olympiad Adventure

Find all natural number \(n\) such that \(n\), \(n^2 + 10\), \(n^2 - 2\), \(n^3 + 6\), \(n^5 + 36\) are all prime numbers.

Note by Dev Sharma
1 year, 9 months ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

Note to self: 1 is not a prime number. Calvin Lin Staff · 1 year, 9 months ago

Log in to reply

This is from the First HK TST. Sualeh Asif · 1 year, 7 months ago

Log in to reply

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 ? Sachin Vishwakarma · 1 year, 9 months ago

Log in to reply

@Sachin Vishwakarma Every odd number (not necessarily prime) is representable in the form \( 4k \pm 1 \) for a suitable k. Calvin Lin Staff · 1 year, 9 months ago

Log in to reply

@Calvin Lin And for \( 6k \pm 1 \) ? Sachin Vishwakarma · 1 year, 9 months ago

Log in to reply

@Sachin Vishwakarma Yes every prime is representable in the form \(6k\pm 1\).

Proof: \(6k, 6k +2,6k+4\) are divisible by 2

\(6k+3\) is divisible by 3 Sualeh Asif · 1 year, 7 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...