Notifications
Clear all
Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.
Real Numbers
1
Posts
2
Users
0
Likes
145
Views
0
24/05/2021 11:25 am
Topic starter
Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.
Answer
Add a comment
Add a comment
Topic Tags
1 Answer
0
24/05/2021 11:25 am
Let a be any positive integer and b = 6. Then, by Euclid’s algorithm, a = 6q + r, for some integer q ≥ 0, and r = 0, 1, 2, 3, 4, 5, because 0≤ r < 6.
Now substituting the value of r, we get,
If r = 0, then a = 6q
Similarly, for r = 1, 2, 3, 4 and 5, the value of a is 6q+1, 6q+2, 6q+3, 6q+4 and 6q+5, respectively.
If a = 6q, 6q + 2, 6q+4, then a is an even number and divisible by 2. A positive integer can be either even or odd.
Therefore, any positive odd integer is of the form of 6q+1, 6q+3 and 6q+5, where q is some integer.
Add a comment
Add a comment
Forum Jump:
Related Topics

The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form, p q what can you say about the prime factors of q? (i) 43.123456789 (ii) 0.120120012000...
3 years ago

Without actually performing the long division, state whether the following rational numbers (i) 23/(2^35^2) (ii) 129/(2^25^77^5) (iii) 6/15 (iv) 35/50
3 years ago

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a nonterminating repeating decimal expansion: (i) 13/3125 (ii) 17/8 (iii) 64/455
3 years ago

Prove that the following are irrationals: (i) 1/√2 (ii) 7√5 (iii) 6 + √2
3 years ago

Prove that 3 + 2√5 is irrational.
3 years ago
Forum Information
 321 Forums
 27.3 K Topics
 53.8 K Posts
 0 Online
 12.4 K Members
Our newest member: Stripchat
Forum Icons:
Forum contains no unread posts
Forum contains unread posts
Topic Icons:
Not Replied
Replied
Active
Hot
Sticky
Unapproved
Solved
Private
Closed