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Home / Elementary Number Theory / The square of any odd integer is of the form 8k +1.

The square of any odd integer is of the form 8k +1.

Solution: Let a is any integer. According to question every a is of the form

8q + 1.

Let, a = 8q + 1

⟹ a2 = (8q +1)2

⟹ a2 = 64q2 + 16q + 1

⟹ a2 = 8(8q2 + 2q) + 1

Let, k = 8q2 + 2q

So, a2 = 8q + 1

Therefore the square of any odd integer is of the form 8k +1.

 

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