Waste less time on Facebook — follow Brilliant.
×

OPC 2 Problem 3

\(3. If \quad [a,b] = (a,b) . \text{ Then show that } a = \pm b.\) [a,b] means LCM. (a,b) means GCD.


Give different methods of solving this. This was a problem to the OPC 2. The OPC 2 has already ended. OPC 3 will be released soon.Calvin sir suggested me to do this.So Thanks to him.\(\ddot\smile\)

Note by Rajdeep Dhingra
2 years, 7 months ago

No vote yet
1 vote

  Easy Math Editor

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 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

This is easy. In fact

\[\left. (a,b) \right\vert a \left\vert [a,b] \right. = (a,b) \qquad \textrm{ where } \big\vert \textrm{ means } divides \]

This means \(a= \pm(a,b)\).

Same holds for \(b\), so \(a = \pm b\).

Andrea Palma - 2 years, 7 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...