Question

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

Answer 1

Hello ,
Answer here ......
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SOL.

Let take a as any positive Integer and b = 6

Than using Euclid's Algorithm
we get a = 6q+r here , r is remainder and value of q is more than or equal to 0 and r = 0,1,2,3,4,5 because 0≤r<B and the value of b is 6

so, total possible forms will 6q+0, 6q+1, 6q+2, 6q+3, 6q+4, 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 divisible by 2 , so it is odd number.

6q+2
6 is divisible by 2 and 2 is also divisible by 2 , so it is even number .

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

6q+4
6 is divisible by 2 and 4 is also divisible by 2, so it is an even number.

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

SO , ODD NUMBERS WILL BE 6q+1 , 6q+3 , and 6q+5 .
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Hope it's helps you.
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