perplexus.info :: Just Math : Prime pair

Prime pair (Posted on 2023-11-17)

Find all pairs (p,q) of prime numbers such that

p(p²-p-1)=q(2q+3)

No Solution Yet Submitted by Danish Ahmed Khan

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solution

| Comment 1 of 3

(p=13, q=31) is the only solution testing primes up to 10,000

primes = [p for p in range(10000) if isprime(p)]

for p in primes:

for q in primes:

if p*(p**2-p-1) == q*(2*q+3):

print('(p={}, q={})'.format(p,q))

note:

Even if you allow non-primes, all integers including zero and negatives, there are not that many solutions (testing up to 10,000):

(p=-1, q=-1)

(p=0, q=0)

(p=1, q=-1)

(p=2, q=-2)

(p=4, q=4)

(p=13, q=31)

(p=35, q=-145)

(p=81, q=-513)

Posted by Larry on 2023-11-17 11:15:19

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