If n^2+7=a^5, and n^3-516=b^2, with a,b,n all positive integers, find a,b, and n.
Prove this solution is unique.
181^2 + 7 = 8^5
181^3 - 516 = 2435^2
(a,b,n) = (8, 2435, 181)
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squares = [i**2 for i in range(10000)]
fifths = [i**5 for i in range(10000)]
for n in range(100000):
if n**2 + 7 in fifths and n**3 - 516 in squares:
print(n, n**2+7, (n**2+7)**.2, n**3-516, (n**3-516)**.5)
Program output:
181 32768 8.000000000000002 5929225 2435.0
[Edited to add program output and second equation]
Edited on September 28, 2023, 3:01 pm
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Posted by Larry
on 2023-09-28 12:26:03 |
Answer without proof of uniqueness
