proofs: divisibility

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if a,b and c are integers such that a divides b and b divides c, then a divides (b squared + c squared). 

Apr 6th, 2015

Since a divides b and b divides c, we can write,

b/a = k

c / b = p

To prove: a divides ( b^2 + c^2 )

b^2 + c^2 / a

Clearly first term will be easily divisible by a ( b /a ) b = k . b will be the resultant

c ^2 = ( p b ) ^2 = p^2 . b ^2 which when divided by a will give = p^2 . b ^2 / a = p ^2 . kb

Hence both the terms are divisible by a.

Hence proved.




Apr 6th, 2015

im confused?


Apr 6th, 2015

That was not how i learned to do divisibility. This is for test corrections. 

Apr 6th, 2015

You need more explanation on it...


If you can send me your solution, I can definitely explain you.

Apr 6th, 2015

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Apr 6th, 2015
Jun 28th, 2017
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