A question about factoring and factors

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    Factoring Factors
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SUMMARY

The discussion centers on the mathematical problem of factoring a number N, expressed as N=pq, where only the last two digits of the factors p and q are known. The participants conclude that it is not possible to uniquely determine the other digits of the factors with just the last two digits, particularly when N is large. The equation N = 10000mn + 100(ms + nr) + rs illustrates the complexity of the problem, indicating that two unknowns (m and n) cannot be solved with a single equation.

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epsi00
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say we have a number N=pq (known) and we only know the last digits of the two factors p and q ( the righter most digit of each factor ). Is-it possible to determine the other digits of the factors? If not, what is the minimum number of digits that should be known before the answer can be a yes?
 
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If N is big enough, I suspect the answer is no.
Let p=100m + r, q=100n + s, where r,s < 100 (all integers).
Then N = 10000mn + 100 (ms + nr) + rs.
You now have one equation (N=) with 2 unknowns (m and n). I don't believe you can find a solution in general.
 

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