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Questions tagged [factoring]

This tag describes challenges related to factoring numbers and polynomials. Not related to the Factor programming language.

16 votes
17 answers
1k views

Echo numbers (A383896) are positive integers k such that the largest prime factor of k-1 is a suffix of ...
ZaMoC's user avatar
  • 25.5k
11 votes
13 answers
1k views

For prime p, the factorization tree is a single vertex in just one way so that a(p) = 1. For composite n, the two subtrees at n are a split of n into two factors n = d * (n/d), without order, so that $...
Sophia Antipolis's user avatar
10 votes
5 answers
2k views

Input The code should take an integer \$n\$ between 1 and 1000. Output The code should output positive integers with \$n\$ bits. Accompanying each integer should be its full factorization. Each ...
Simd's user avatar
  • 3,167
13 votes
25 answers
1k views

The Prime Signature of a number is the list of the exponents of the prime factors of a number, sorted in descending order (exponents of 0 are ignored). Inspired by ...
Samathingamajig's user avatar
17 votes
11 answers
1k views

Carryless multiplication is an operation similar to binary long multiplication, but with XOR instead of addition: ...
rydwolf's user avatar
  • 19.3k
12 votes
7 answers
900 views

Though there is a prime factorization challenge and it's here, this, I feel, will be a bit more interesting than that one. To understand this, let's have an example; I will use 5,184 for this. \$5184 =...
user avatar
0 votes
4 answers
281 views

Although there was a prime factors challenge posted ten years ago, it has tedious I/O and restricted time. In this challenge, your task is to write a program or function which takes an integer \$n \ge ...
rydwolf's user avatar
  • 19.3k
10 votes
8 answers
491 views

Create the shortest function, program, or expression that calculates a sequence of squarefree palindromic numbers. A squarefree number is one which is not evenly divisible by a square number (i.e. ...
Neel Shukla's user avatar
23 votes
28 answers
3k views

When learning to factorise quadratics in the form \$x^2 + ax + b\$, a common technique is to find two numbers, \$p, q\$ such that $$pq = b \\ p + q = a$$ as, for such numbers, \$x^2 + ax + b = (x + p)(...
caird coinheringaahing's user avatar
32 votes
20 answers
3k views

Figuring out whether a given number is prime, while not very complicated, is kind of hard. But making a guess doesn't need to be. Seeing whether a number is a multiple of 2 or 5 is easy - you can just ...
Sara J's user avatar
  • 3,855
-7 votes
1 answer
214 views

Create a function which takes in a input integer and then returns the number of factors it has, like if you pass 25 then it will return ...
Smilecat's user avatar
  • 165
14 votes
11 answers
923 views

Output Distinct Factor Cuboids Today's task is very simple: given a positive integer, output a representative of each cuboid formable by its factors. Explanations A cuboid's volume is the product ...
lyxal's user avatar
  • 35.6k
29 votes
18 answers
4k views

Since Euclid, we have known that there are infinitely many primes. The argument is by contradiction: If there are only finitely many, let's say \$p_1,p_2,...,p_n\$, then surely \$m:=p_1\cdot p_2\cdot.....
flawr's user avatar
  • 44.1k
10 votes
0 answers
314 views

I need to construct a functor that iterates over the linear representation of a sub-lattice of size \$d_x,d_y,d_z,d_q\$ embedded in a lattice of size \$n_x,n_y,n_z,n_q\$. The sub-lattice corner is ...
user3646557's user avatar
2 votes
1 answer
232 views

If I need to get the number of diagonal squares in all directions: I do the following formula 2 N − 2 − |x − y| − |x + y − N − 1| The above example has 13 and that'...
Ibrahim Ali's user avatar

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