Question

Show that the square of any positive odd integer is of the form 8n + 1 , for some integer n​

Answer 1

hope it will help you

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Answer 2

Answer:

Yes it is

Step-by-step explanation:

we know that,

a=bq+ r

where, r >=0 and smaller than b

So for r =0,1,2,3,4,5,6,7

for r=0

a= 8n+0

a^2 =( 8n+0)^2

a^2= 8n^2+2(8n×0)+0^2

a^2=64n^2

a^2= 8(8n^2)

a^2=8n

for r=1

a=8n+1

a^2=(8n+1)^2

=8n^2 + 2(8n×1)+1^2

=64n^2 + 16n+1

=8(8n^2+2n)+1

=8n+1

hence proved