Probably just a rule

Level pending

If a^x = b^x Where a and b are integers , x is also an integer with (x/2) also being an integer Is a always equal to b?

No Yes

1 solution

Rahul Singh
May 18, 2015

Since X/2 is an integer, therefore X must be an even integer.

Now let X=2k, for some odd integer k. Therefore,

              a^(2k)=b^(2k)

        Or, (a^k)^2=(b^k)^2

        Or, (a^k)= +(b^k), - (b^k)

        Or, a= +b, -b

Hence, 'a' is not necessarily equal to 'b'.