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A306666 Positive integers x such that x*(7-5*x+x^2)*(6-4*x+x^2) is a square. 0

%I #15 Nov 25 2019 01:06:35

%S 1,2,3,7,21

%N Positive integers x such that x*(7-5*x+x^2)*(6-4*x+x^2) is a square.

%C No other terms below 10^6.

%C No other terms below 10^10. - _Chai Wah Wu_, Nov 24 2019

%H dxdy forum, <a href="https://dxdy.ru/post1379764.html">x(7-5x+x^2)(6-4x+x^2)=y^2 in natural numbers</a> (in Russian).

%t Select[Range[1000], IntegerQ[Sqrt[#*(7 - 5*# + #^2)*(6 - 4*# + #^2)]] &] (* _Vaclav Kotesovec_, Mar 10 2019 *)

%o (PARI) isok(x)=issquare(x*(7-5*x+x^2)*(6-4*x+x^2));

%o (Python)

%o from sympy.ntheory.primetest import is_square

%o A306666_list = [n for n in range(1,10**3) if is_square(n*(n*(n*(n*(n - 9) + 33) - 58) + 42))] # _Chai Wah Wu_, Nov 24 2019

%K nonn,more

%O 1,2

%A _Dmitry Ezhov_, Mar 04 2019

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