Question

show that any positive odd integer is of the 6q + 1 or 6 + 3 or 6 + 5 for some integer​

Answer 1

Step-by-step explanation:

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Question :-

show that any positive odd integer is of the 6q + 1 or 6 + 3 or 6 + 5 for some integer.

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Given :-

• The 6q + 1 or 6 + 3 or 6 + 5 for some integer.

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To Find :-

• show that any positive odd integer

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Any positive odd integer is of form 2p +1, where p is an integer.

Now,

According to the Question :-

6q + 1= 2×(3q) +1

6q + 3 = 2×(3q +1) + 1

6q + 5 = 2×(3q +2) +1

So all the above three are positive odd number ,

When an odd number is divided by 6, then it should have remainder = 1, (1+2)=3, (1+2+2)=5

Thus, 6q +1, 6q+3, 6q +5 represent all positive odd numbers.