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(1) Sum of two factorials in two ways; (2) Value of $a^{2010}+a^{2010}+1$ given $a^4+a^3+a^2+a+1=0$.
Question $1$:
Does there exist an integer $z$ that can be written in two different ways as $z=x!+y!$,where $x,y\in \mathbb N$ and $x\leq y$?
Answer: $0!=1!$ so $0!+2!=3=1!+2!$
Question $2$:
If $...
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Reasoning about a sequence of consecutive integers and factorials with hope of relating factorials to primorials
I am looking for someone to either point out a mistake or help me to improve the argument in terms of clarity, conciseness, and more standard mathematical argument.
Let $x$ be an integer such that $x,...
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