1.

Can we have any n £ n , where 7power n ends with the digits zero

Answer»

Let , if possible 7^n ends with digits ZERO

As 7^n ends with DIGIT zero
=> 7^n must have factor 2 and 5 ----(i)

but according to fundamental theorem of arithmetic, it gaurantees that 7 ^n can have only factor as multiple of 7 ----(ii)

(i) and (ii) CONTRADICTS each other
Thus 7^n can never end with digit zero for any natural number n...


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