perplexus.info :: Just Math : 27-8=19

27-8=19 (Posted on 2015-03-31)

19 is the only prime which is equal to the difference of two cubes of primes.

Prove the above statement.

See The Solution Submitted by Ady TZIDON

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

Solution

| Comment 1 of 3

p^3-q^2=(p-q)(p^2+pq+q^2)

The difference of cubes is only prime if one of the factors is 1.

p^2+pq+q^2 > 1 for any primes

p-q=1 only for p=3, q=2 as they are the only primes that differ by 1.

Posted by Jer on 2015-03-31 11:59:48

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info