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प्रश्न
Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.
उत्तर
No, every positive integer cannot be of the form 4q + 2, where q is an integer.
Justification:
All the numbers of the form 4q + 2
Where ‘q’ is an integer, are even numbers which are not divisible by ‘4’.
For example,
When q = 1
4q + 2 = 4(1) + 2 = 6
When q = 2
4q + 2 = 4(2) + 2 = 10
When q = 0
4q + 2 = 4(0) + 2 = 2 and so on.
So, any number which is of the form 4q + 2 will give only even numbers which are not multiples of 4.
Hence, every positive integer cannot be written in the form 4q + 2
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