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Near powers (Posted on 2023-09-28)

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.

No Solution Yet Submitted by broll

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computer solution -- no proof of uniqueness

Comment 2 of 2 |

clearvars,clc

for n=1:9999

for a=1:9999

if n^2+7==a^5

for b=1:9999

if n^3-516==b^2

disp([a b n])

disp([a^5 b^2])

disp(' ')

end

finds

a = 8; b = 2435; n = 181

a^5 = 32768; b^2 = 5929225

Posted by Charlie on 2023-09-28 12:32:28

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