Interesting Multiplication

Number Theory Level pending

1 × 2 × . . . × 2006 × 2007 = a × 2 n = b × 10 m 1\times 2\times ...\times 2006\times 2007=a\times { 2 }^{ n }=b\times { 10 }^{ m } where a is a odd number integer, and b is any integer that is not a multiple of 10, and n,m is an integer. Find the value of n+m


The answer is 2498.

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