+0  
 
0
258
3
avatar+557 

thank you in advance

 

winkwinkwink

 Apr 19, 2018
 #1
avatar+972 
+3

I think I can give it a go!

 

Proof : By the division theorem any number can be expressed in one of the forms 4q,4q+1,4q+2,4q+3

 

After squaring each of the odd expressions :


\((4q+1)^2= 16q^2+8q+1=8(2q^2+q)+1 \)

 

\((4q+3)^2=16q^2+24q+9=8(2q^2+3q+1)+1\)

 

As shown here, it can be expressed as 8 times a number, then added by one. 

 

I hope this helps!

 Apr 19, 2018
 #2
avatar+98198 
+2

Very nice, Gavin....!!!!

 

 

cool cool cool

CPhill  Apr 19, 2018
 #3
avatar+972 
0

Thank you!

GYanggg  Apr 19, 2018

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