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Prove that if a positive integer …

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Prove that if a positive integer is of the form 6q+5,then it is of the form 3q+2 for some integer q,but not conversely

Posted by Nikky Garg 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Let n = 6q + 5, where q is a positive integer.
We know that any positive integer is of the form 3k or, 3k +1 or, 3k + 2.
{tex}\therefore{/tex} q = 3k or, 3k + 1 or, 3k + 2.
If q = 3k, then,we have,
n = 6q + 5 = 18k + 5 = 3 (6k + 1) + 2 = 3m + 2, where m = 6k + 1
If q = 3k + 1, then
n = 6q + 5 = 6 (3k + 1) + 5 = 3 (6k + 3) + 2 = 3m + 2, where m = 6k + 3
If q = 3k + 2, then
n = 6q + 5 = 6 (3k + 2) + 5 = 3 (6k + 5) + 2 = 3m + 2, where m = 6k + 5.

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CBSE > Class 10 > Mathematics