Question 1068303
If {{{x>1}}} is a positive integer,
{{{x^2-x=x(x-1)}}} is the product of two consecutive integers,
so one of those integers must be even,
so the product must be even.
Either {{{x=2n}}} is even,
with {{{n}}} being a positive integer,
and {{{x(x-1)=2n(x-1)}}} is a multiple of 2,
or dividing {{{x}}} by 2 there is a quotient {{{q}}} and a remainder {1} .
In that case, {{{x=2q+1}}} , {{{x-1=2q}}} ,
and {{{x(x-1)=(2q+1)*2q}}} is a multiple of 2.