# Tagged Questions

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### Any simpler way to do Pollard's p-1 method?

I found calculating factorization by Pollard's p-1 method is almost impossible if use a conventional scientific calculator. For example, I am trying to factor ...
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### How does a Lehmer Sieve work?

http://en.wikipedia.org/wiki/Lehmer_sieve Apparently a Lehmer Sieve was a mechanical device that used chains and pulleys to factor numbers and solve diophantine equations. It once was able to factor ...
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### If $a^4+b^4\in\mathbb Q$ and $a^3+b^3\in\mathbb Q$ and $a^2+b^2\in\mathbb Q$, prove that $a+b\in\mathbb Q$ and $ab\in\mathbb Q$.

If $\begin{cases}a^4+b^4\in\mathbb Q\\ a^3+b^3\in\mathbb Q\\ a^2+b^2\in\mathbb Q\end{cases}$, prove that $a+b\in\mathbb Q$ and $ab\in\mathbb Q$. It is given that $a,b\in\mathbb R$. The proof of ...
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### Sums and differences of distinct factors

Given $k, n \in \mathbb{N}$, let $\tau_{k}(n)$ denote the $k$th positive factor of $n$ in strictly increasing order. For example, $\tau_{1}(6) = 1; \tau_{2}(6) = 2; \tau_{3}(6) = 3; \tau_{4}(6) = 6$. ...
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### Determine the largest power of 10 that is a factor of $50!\,$?

How would one find the largest power of 10 which is a factor of $50!\,{}$?
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### What is the line of thinking to get $[(n^2+3n+1)^2-5n(n+1)^2]$ from $(n^4+n^3+n^2+n+1)$?

There is this one little tiny step along the working that I don't quite understand, but I think it is better if I write the whole problem and solution for clarity. Problem: Factorise $5^{1995}-1$ ...