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Show that every positive odd integer …

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Show that every positive odd integer is of the form (4q+1) or (4q+3) for some integer q.

Posted by Pransh Yadav 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Let a = 4q + r : 0 {tex}\leq r < 4{/tex}
{tex}\therefore a = 4 q = 2 ( 2 q ) \text { an even integer }{/tex}
{tex}a = 4 q + 1 = 2 ( 2 q ) + 1 \text { an odd integer }{/tex}
{tex}a = 4 q + 2 = 2 ( 2 q + 1 ) \text { an even integer }{/tex}
{tex}a = 4 q + 3 = 2 ( 2 q + 1 ) + 1 \text { an odd integer }{/tex}
{tex}\therefore {/tex} Every positive odd integer is of the form
{tex}( 4 q + 1 ) o r ( 4 q + 3 ) \text { for some integer }{/tex}

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CBSE > Class 10 > Mathematics