Can we define parity & primality for negative numbers?

1st Part: Can we define a negative number as even or odd?

I think it would be yes because any negative number when divided by 2 either leaves remainder of 0 and 1. I need suggestions about it.

2nd Part: The second part is tricky: Can we define a negative number to be prime or Composite?

If I define positive prime number as follows: An positive Integer having exactly two positive distinct factors. Then 2, 3, 5, 7,.... would be prime and 0, 1, 4, 6,.... would not be prime. If we take -2, it would have infinitely distinct factorizations: -2 = (-1)(2); -2 = (1)(-2); -2 = (-1)(-1)(-1)(2);...... and it doesn't obey fundamental theorem of Arithmetic since it isn't unique. Similarly taking prime factorizations of any negative Integer always give multiple factorizations. So, negative numbers couldn't be defined to be prime or composite in the same way as positive Integer greater than 1.

My real question is 'If I want to define "Negative Prime" in a different way, then how can I do it'?

Note by Vaibhav Priyadarshi
1 year 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]( 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} \( \boxed{123} \)


Sort by:

Top Newest

Yes, you can do all that. If you study ring theory, these things are well understood.

Agnishom Chattopadhyay Staff - 1 year ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...