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Mixed square (Posted on 2021-06-18)

Find all positive integers n such that (n² + 11n - 4)n! + 33*13ⁿ + 4 is a perfect square.

No Solution Yet Submitted by Danish Ahmed Khan

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re: partial answer

| Comment 2 of 5 |

(In reply to partial answer by Larry)

These remain the only two answers through n=300:

digits 1000

for n0=1:300

n=vpa(n0);

v=(n*n+11*n-4)*factorial(n)+33*vpa(13)^n+4;

sr=round(sqrt(v));

if sr*sr==v

disp ([sr n v sr*sr])

end

sets show square root, n and f(n) twice.

[ 21, 1.0, 441.0, 441]

[ 75, 2.0, 5625.0, 5625]

Posted by Charlie on 2021-06-18 13:25:53

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