Q. 395.0( 1 Vote )

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

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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