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If a and b are coprime, then a2 and b2 a^2\, and \,b^2 a2andb2​are-
Question

If a and b are coprime, then a2 and b2 a^2\, and \,b^2 ​are-

A.

Coprime

B.

Both even

C.

Need not be coprime

D.

Both odd

Correct option is A

Solution:

Two numbers are said to be coprime if their greatest common divisor (GCD) is 1. In other words, they share no common prime factors. If aaa and bbb are coprime, squaring them does not introduce any new common factors. Therefore, a2 and b2a^2 \, and \, b^2​will also have no common factors and will remain coprime.

Hence, a2 and b2a^2 \, and \, b^2are coprime.

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