# Tagged Questions

116 views

### Defining irreducible polynomials recursively: how far can we go?

Fix $n\in\mathbb N$ and a starting polynomial $p_n=a_0+a_1x+\dots+a_nx^n$ with $a_k\in\mathbb Z\ \forall k$ and $a_n\ne0$. Define $p_{n+1},p_{n+2},\dots$ recursively by $p_r = p_{r-1}+a_rx^r$ such ...
89 views

### Number of divisors of a number

Is there any trick to find the number of divisors of any number? For e.g., a quick way to tell the number of divisors of 987655432 (chosen randomly)? EDIT: And it has to be done without prime ...
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### Number of factors of a big number

what is the number of the factors of 884466000.how can I do this math without using factoring calculator?
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### Divisibility and factors [duplicate]

1) Can factors be negative? Please prove your opinion. 2)If prime factorization is given to you, how will you find out how many composite factors are there? Not the factors, just how many. For 2), my ...
158 views

### Simplifying $\sqrt{\underbrace{11\dots1}_{2n\ 1's}-\underbrace{22\dots2}_{n\ 2's}}$

How do I simplify: $$\sqrt{\underbrace{11\dots1}_{2n\ 1's}-\underbrace{22\dots2}_{n\ 2's}}$$ Should I use modulos or should I factor them? Or any I suppose to use combinatorics? Any one have a ...
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### Is there any known algorithm for factoring the fractional components of a binomial?

For a binomial such as $\binom {15} {6}=\frac{15\times14\times13\times12\times11\times10}{6\times5\times4\times3\times2\times1}$, it seems that it always divides evenly into an integer, and I ...
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### If $A,B$ are factors of $2^6 3^4 5^2,$ how many values of $|A-B|$ are possible?

Let $x=2^6 3^4 5^2$, then how many distinct values of $|A-B|$ are possible where $A, B$ are the factors of $x$? How to approach this problem?
How do I approach this problem using unique factorization?... How many numbers are product of (exactly) $3$ distinct primes $< 100$? edit: Just to add to that, How does unique factorization ...
I need to find the number of factors of a large number $n^2$ that are less than $n$. Supposing I can find the prime factorization, it is simple to find the total number of factors as a combinatorial ...