Factors on N^3

Computer Science Level 5

Let N = 579 1 3 ⋅ 580 1 2 ⋅ 580 7 4 N = 5791^3\cdot 5801^2\cdot 5807^4 be a prime factor decomposition.

How many positive integers less than N N are divisors of N 3 N^3 but not of N N ?


The answer is 129.

Arjen Vreugdenhil by Arjen Vreugdenhil , 44, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
 
final int A = 5791, B = 5801, C = 5807;

double lA = log(A), lB = log(B), lC = log(C);
double lN = 3*lA + 2*lB + 4*lC;

int count = 0;

for (int a = 0; a <= 9; a++) for (int b = 0; b <= 6; b++)
    for (int c = 0; a+b+c <= 9; c++) 
        if (a > 3 || b > 2 || c > 4) {
            double lD = a*lA + b*lB + c*lC;
            if (lD < lN) count++;
    }

out.println(count);

Output: 

1
 
129

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Bob Kadylo
Dec 22, 2016

I was using Python in SAGE here

What William Stein, his students, and many collaborators have developed is an OpenSource Environment that, in many ways, accomplishes the same as Mathematica, MatLab, Magma, Maple or Maxima - but you know their cost !!

SAGE is not as fancy but very powerful (and the price is right) !!

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Aareyan Manzoor
Jan 22, 2016

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Not quite sure how SFFT factors in here (no pun intended).

Arjen Vreugdenhil - 5 years, 4 months ago

Log in to reply

Lol i just realized it doesn't!

Aareyan Manzoor - 5 years, 4 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...