show that the square of an odd positive integer is of the form 8q+1 for some integer q
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Thus so
Let any odd positive integer of be the form a = bq + r
Where
R = 3 .2 .1 .0
R = 3 .1 as odd
Thus
a = ' 4q + 3 ' ²
. 16q² + 24q + 8 + 1
. 8 ' 2q² + 3q + 1 ' + 1
. 8 q + 1
thus
. a = ' 4q + 1 ' ²
. 16q² + 8q + 1
. 8 ' 2q² + q ' + 1
. 8 q + 1
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Let any odd positive integer of be the form a = bq + r
Where
R = 3 .2 .1 .0
R = 3 .1 as odd
Thus
a = ' 4q + 3 ' ²
. 16q² + 24q + 8 + 1
. 8 ' 2q² + 3q + 1 ' + 1
. 8 q + 1
thus
. a = ' 4q + 1 ' ²
. 16q² + 8q + 1
. 8 ' 2q² + q ' + 1
. 8 q + 1
Mark as brainliest if helpful
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