Posted by **priya** on Sunday, June 21, 2009 at 4:40am.

show that any positive odd integer is of the form 6q+1, 6q+3 or 6q+5, where q is any positive integer.

- math -
**drwls**, Sunday, June 21, 2009 at 6:03am
The positive integers +1, +3 and +5 are not of that form, unless q can also be zero.

The difference between 6q + 5 and 6q' +1, if q' = q+1 , is

[6(q+1) + 1]-[6q +5] = 2

That means that by increasing q by 1 when you get to 6q+5, the next number will be 2 greater, so that all odd numbers can be created. All one has to do is pick the next integer q when you get to 6q +5, and start over at 6q' +1

## Answer this Question

## Related Questions

- DISCRETE MATHS - We need to show that 4 divides 1-n2 whenever n is an odd ...
- math - Show that any positive odd integer is of the form 6q+1, 6q+3 or 6q+5, ...
- MATH - Find the only positive integer whose cube is the sum of the cubes of ...
- math - show that any positive integer is of the form 4q, 4q+2, where q is any ...
- math - Show that any positive integer is of the form 4q, 4q+2, where q is any ...
- discrete math - Prove by contradiction that for any even integer a and any odd ...
- Math (Complex Numbers) - Let N be the sum of all prime powers that can be ...
- maths - prove that any odd positive integer of 8q+1,where q is any integer?
- Math - When you add a positive integer and a negative integer, you sometimes get...
- math - If n is a positive integer, then what is the value of (2/3)^n (1 1/2)^n-1...