Question

show that any positive odd integer is of the form 6p + 1 or 6p + 5 where p is some integer

Answer 1

Hii friend,

Let n be a given positive odd integer.

On dividing n by 6 , let Q be the Quotient and r be the reminder.

Then , by Euclid's division lemma , we have

=> N = 6Q+r , Where r = 0,1,2,3,4,5

=> N = 6Q or (6Q+1) or (6Q+2) or (6Q+3) or (6Q+4) or (6Q+5) .

But , N = 6Q , (6Q+2) , (6Q+4) are the even values of n.

Thus, when n is odd, it is in the form of (6Q+1) or (6Q+3) or (6Q+5) for some integer Q.


HOPE IT WILL HELP YOU...... :-)

Answer 2

Hello dear,
{Ur answer is here}
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Sol.

By Euclid's Algorithm
a= 6q + r and r = 0,1,2,3,4,5
hence , a = 6q or 6q +1 , 6q +2, 6q +3 , 6q +4 and 6q +5.

=> 6q +0
6 is divisible by 2 , so it is even number.

=> 6q +1
6 is divisible by 2 but 1 is not , so it's odd number.

=> 6q + 2
6 is divisible by 2 and 2 is also divisible by 2 , so it's even number.

=> 6q + 3
6 is divisible by 2 but 3 is not , so it is odd number.

=> 6q +4
6 is divisible by 2 and 4 is also divisible by 2 , so it's even number.

=> 6q + 5
6 is divisible by 2 but 5 is not , so it is odd number.

SO ODD NUMBER WILL BE. 6q + 1 , 6q + 3 , 6q+ 5.
hence , these numbers are odd position NUMBERS.
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Hope it's helps you.
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