Question

 Show that any positive odd integer is of the form (6p+1), (6p+3) or (6p+5), where p is some integer.​

Answer 1

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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.

Answer 2

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