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It is known that if a_{s}k^{s}+a_{s-1}k^{s-1}+...+a_{0}is a representation of n to the base k, then 0<n<=k^{s+1}-1.

Now suppose n=a_{s}k^{s}+a_{s-1}k^{s-1}+...+a_{0}and m=b_{t}k^{t}+b_{t-1}k^{t-1}+...+b_{0}with a_{s},b_{t}not equal to 0, are two different representations of n and m to base k, respectively. Without loss of generality we may assume t>=s. Without using Theorem 1-3(existance and uniqueness of such representation of an integer), prove directly that m not equal to n.

Many many thanks~~~

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# Base representation ~

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