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.

Submitted by Ady TZIDON

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Solution: (Hide)

p^3-q^2=(p-q)(p^2+pq+q^2) ,therefore
p-q must be 1, so p=3, q=2 and the answer 3^3-2^3=27-8=19

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Solution	K Sengupta	2022-05-16 23:13:50
re: Solution ...........add the conclusion	Ady TZIDON	2015-04-01 09:53:59
Solution	Jer	2015-03-31 11:59:48

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