perplexus.info :: Just Math : Cubes in either side

Cubes in either side (Posted on 2025-04-09)

Find all triples (m, n, p) satisfying

(m³ + n)(n³ + m) = p³

where m, n are positive integers and p is a prime number

No Solution Yet Submitted by Danish Ahmed Khan

No Rating

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

Computer solution

Comment 1 of 1

(m, n, p)

(1,2,3)

(2,1,3)

-------

p3s = [i**3 for i in range(1000) if isprime(i)]

big = 1000

print('(m, n, p)')

for m in range(1, big+1):

for n in range(-big, big+1):

lhs = (m**3 + n)*(n**3 + m)

if lhs not in p3s:

continue

p = round( lhs ** (1/3) )

print('({},{},{})'.format(m,n,p))

Posted by Larry on 2025-04-09 15:00:58

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (9)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info