Q. 395.0( 1 Vote )

Prove if 3 | (a2 + b2) then 3 |a and 3| b, a N, bN.

Answer :

Let us suppose 3 is a factor of a and b.


Therefore, we can write a = 3k and b = 3m


Now, a2 + b2 = (3k)2 + (3m)2


= 9k2 + 9m2


= 3(3k2 + 3m2)


Therefore it is divisible by 3.


So, 3 is a factor of a2 + b2


Similarly, the reverse condition is also true.


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