easy one

Prove if gcd(a,b)=1,then gcd(a^2,b^2)=1.

1 Answers

a=p_1^\alpha p_2^\beta p_3^\gamma ...

b=P_1^\alpha P_2^\beta P_3^\gamma ....

Needless to mention p_i's & P_i's are primes.

Since P_i\ne p_j for any (i,j), g.c.d(a²,b²)=1 as well, as prime factors of a² and b² are same.

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