perplexus.info :: Just Math : Prime power pair

Prime power pair (Posted on 2023-10-08)

Solve the equation in prime numbers

p³-q⁵=(p+q)²

No Solution Yet Submitted by Danish Ahmed Khan

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I found ... (completeness not proven)

| Comment 1 of 2

(p,q) = (7,3) and (0,-1) are the only solutions I found.

----------------------------

for q in range(-1000,1000):

if q == 0:

continue

q5 = q**5

sign = q5 / abs(q5)

minp = sign * (abs(q5)**(1/3))

if minp**3 - q**5 < 0:

minp = int(minp)

else:

minp = int(minp) + 1

for p in range(minp,minp+1000):

if p**3-q**5 == (p+q)**2:

print(p,q)

Posted by Larry on 2023-10-08 09:20:35

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