Factorization

(Medium) Let a, b and c be nonzero integers, with 1 as their only positive common divisor, such that 1a+1b+1c=0\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 0. Find the number of such triples (a,b,c)(a, b, c) with 50abc150 \geq \mid a \mid \geq \mid b \mid \geq \mid c \mid \geq 1

Note by Cai Junxiang
1 week, 6 days ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

The answer to your question is 66 I found it by a python program do you want to see it?

Sahar Bano - 1 week ago

Log in to reply

Sure

Cai Junxiang - 6 days, 13 hours ago

Log in to reply

The answer should be an even number because if (a,b,c) is a solution, so is (-a,-b,-c) i.e. solutions come in twos. Brute force with a computer program identified these 22 solutions: -45,-36,20 -42,-7,6 -40,-24,15 -35,-14,10 -30,-6,5 -28,-21,12 -20,-5,4 -15,-10,6 -12,-4,3 -6,-3,2 -2,-2,1 2,2,-1 6,3,-2 12,4,-3 15,10,-6 20,5,-4 28,21,-12 30,6,-5 35,14,-10 40,24,-15 42,7,-6 45,36,-20 All have the pattern that a and b have the same sign and c has the opposite sign. The most common solution has the pattern (n(n+1),n+1,-n) - or the same pattern with the signs switched. There are other solutions though. I'm not sure if there is a more elegant way to solve this than brute force.

Justin Travers - 6 days, 13 hours ago

Log in to reply

I don’t know anything can be better than a great service that will help you write your article or essay on any topic as soon as you want. <a href=https://grademiners.com/>Grade Miners</a>

Mike Jason - 5 days, 11 hours ago

Log in to reply

In science, factorization or considering comprises of composing a number or another scientific article as a result of a few variables ArchLooks.com, typically littler or less difficult objects of a similar kind. For instance, 3 × 5 is a factorization of the whole number 15, and is a factorization of the polynomial x² – 4.

Alisa Ava - 4 days, 20 hours ago

Log in to reply

Adeno-associated virus (AAV) has been widely used by scientists to deliver exogenous genetic material into cultured cells or live animal models. https://www.creative-biogene.com/Services/Custom-Viral-Service/AAV-service.html

Creative Biogene - 4 days, 10 hours ago

Log in to reply

At one time I was helped by an excellent article and essay service when I wrote articles for magazines and websites https://papernow.org/mla-style-paper

Mike Jason - 1 week, 3 days ago

Log in to reply

That`s interesting!

Jake Grane - 1 week, 3 days ago

Log in to reply

Thanks for the interesting information! Frankly speaking I am not so good at math, and I can't understand these formulas and calculations, but I think the more people play, the less chance to win, that's why I try to play games where there are not many players. Recently I tried playing syndicate.casino casino Australia, they have a lot of casino games with different numbers of players, and you can choose a game to your preferences. By the way they always offer different bonuses and other profitable rewards.

Jake Grane - 1 week, 3 days ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...