Question

s
show that the square of an odd positive
integer is of from 8q+1 from Some positive integer q​

Answer 1

$\huge\underline\mathcal{Answer}:-$

Given that,

To show that the square of any odd positive integer is of form 8q + 1

Explanation,

As per the Euclid's Division Lemma,

$\boxed{a = bq + r}$

Let a be any positive integer,

b = 8,

Possible remainder can be 1,3,,

If we take remainder as 1

We can write the expression as

⇒a = 8q + 1

By squaring both sides

⇒a² = (8q)² + 1²

⇒a² = 64q² + 1

⇒a² = 8(8q²) + 1

Here b=8, q = (8q)

If we take remainder as 2

We can write the expression as

⇒a = 8q + 3

By squaring both sides

⇒a² = (8q)² + 3²

⇒a² = 64q² + 9

⇒a² = 64q² + 8+1

⇒a² = 8(8q² + 1) + 1

Here b = 8, q = (8q² + 1)

So, By seeing these two situations we can write that the square of any odd positive integer in the form of (8q + 1)

$\boxed{Hence\: Proved//}$

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