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# FindInstance with a DiphantineDiophantine equation seems to go on forever

I tried to find a non-trivial integer solution to the equation
$$2012^2=a^2+b^2+c^2+d^2+e^2$$ with Mathematica but the computation takes minutes, iminutes; I might be doing something wrong.

FindInstance[2012^2 == a^2 + b^2 + c^2 + d^2 + e^2
&& a > 0 && b > 0 && c > 0 && d > 0 && e > 0, {a, b, c, d, e}, Integers]


But when iI try

FindInstance[2012^1 == a^2 + b^2 + c^2 + d^2 + e^2
&& a > 0 && b > 0 && c > 0 && d > 0 && e > 0, {a, b, c, d, e}, Integers]


iI get an immediate result.

# FindInstance with a Diphantine equation seems to go on forever

I tried to find a non-trivial integer solution to the equation
$$2012^2=a^2+b^2+c^2+d^2+e^2$$ with Mathematica but the computation takes minutes, i might be doing something wrong.

FindInstance[2012^2 == a^2 + b^2 + c^2 + d^2 + e^2
&& a > 0 && b > 0 && c > 0 && d > 0 && e > 0, {a, b, c, d, e}, Integers]


But when i try

FindInstance[2012^1 == a^2 + b^2 + c^2 + d^2 + e^2
&& a > 0 && b > 0 && c > 0 && d > 0 && e > 0, {a, b, c, d, e}, Integers]


i get an immediate result.

# FindInstance with a Diophantine equation seems to go on forever

I tried to find a non-trivial integer solution to the equation
$$2012^2=a^2+b^2+c^2+d^2+e^2$$ with Mathematica but the computation takes minutes; I might be doing something wrong.

FindInstance[2012^2 == a^2 + b^2 + c^2 + d^2 + e^2
&& a > 0 && b > 0 && c > 0 && d > 0 && e > 0, {a, b, c, d, e}, Integers]


But when I try

FindInstance[2012^1 == a^2 + b^2 + c^2 + d^2 + e^2
&& a > 0 && b > 0 && c > 0 && d > 0 && e > 0, {a, b, c, d, e}, Integers]


I get an immediate result.

1

# FindInstance with a Diphantine equation seems to go on forever

I tried to find a non-trivial integer solution to the equation
$$2012^2=a^2+b^2+c^2+d^2+e^2$$ with Mathematica but the computation takes minutes, i might be doing something wrong.

FindInstance[2012^2 == a^2 + b^2 + c^2 + d^2 + e^2
&& a > 0 && b > 0 && c > 0 && d > 0 && e > 0, {a, b, c, d, e}, Integers]


But when i try

FindInstance[2012^1 == a^2 + b^2 + c^2 + d^2 + e^2
&& a > 0 && b > 0 && c > 0 && d > 0 && e > 0, {a, b, c, d, e}, Integers]


i get an immediate result.