# Just a Mod Problem...

**Number Theory**Level 3

The number of factors of \({ 10 }^{ ({ 45 }^{ 11 }-1 )}\) is some number x. If

\(x \equiv a \pmod {6} \),

then find the value of "a".

Details and assumptions:

-1 < a < 6 , for "a" an integer.

The number of factors of \({ 10 }^{ ({ 45 }^{ 11 }-1 )}\) is some number x. If

\(x \equiv a \pmod {6} \),

then find the value of "a".

Details and assumptions:

-1 < a < 6 , for "a" an integer.

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