Find the positive integer pair (m, n) such that m*n is the minimum and the last 98 digits in m^m*nⁿ are all zeroes.

Note: 99^th digit from the right in m^m*nⁿ is not zero.

I try to find solution like this :

n=2^a*5^b and m=2^c*5^d,

but after a lot of calculus i can't find these kind of solution.

So i suppose the solution are like n=a*2^b and m=c*5^d

and i found : n=49*2=98 and m=21*5=105 

(m,n) = (105,98)

I'm not sure if this pair provide minimum for m*n!

 

Posted by Chesca Ciprian on 2007-10-27 14:57:03