Determine the only possible integer value of N, such that each of:
8N3-20, and 2N5-2
is a perfect square.
Prove that no further value of N satisfies the given conditions.
**** Computer program/ excel solver assisted solutions are welcome, but a semi-analytic - namely, p&p and hand calculator based methodology is preferred.
for n=1:999
a=8*n^3-20;
sr=round(sqrt(a));
if sr*sr==a
b=2*n^5-2;
sr=round(sqrt(b));
if sr*sr==b
disp([n a b])
end
end
end
finds only
n= 3
The two given expressions are 196 and 484, 14^2 and 22^2 respectively.
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Posted by Charlie
on 2023-09-24 12:51:36 |
answer -- no proof
