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Prove that the 5-adic valuation of $(10^{k+t}+10^t+1)^c-1$ is $t+v_5(c)$
Here is a result of mine that I really wish to be strictly proven (I need it as an intermediate lemma for a theorem).
Let $v_5(a)$ indicate the $5$-adic valuation of $a \in \mathbb{Z}^+$.
How can we ...
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4
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3
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Prove that $x^2+px+p^2$ is a factor $(x+p)^n-x^n-p^n$, if $n$ be odd and not divisible by $3$.
Question:
Prove that $x^2+px+p^2$ is a factor of $(x+p)^n-x^n-p^n$, if $n$ is odd and is not divisible by $3$.
My approach:
$$(x+p)^n-x^n-p^n=\sum_{r=0}^n\limits {n\choose r} x^{n-r}p^r-x^n-p^n$$ What ...
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5
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"Binomial coefficients" generalized via polynomial iteration
This is a question I will answer myself immediately by repeating one of my old AoPS posts, since the latter post no longer renders on AoPS.
Convention. In the following, whenever $A$ is a ...
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