Let *P* equal the product of 3,659,893,456,789,325,678 and 342,973,489,379,256. The number of digits in *P* is:

- 36
- 35
- 34
- 33
- 32

The Ohio State University: College of Education and Human Ecology

Let *P* equal the product of 3,659,893,456,789,325,678 and 342,973,489,379,256. The number of digits in *P* is:

- 36
- 35
- 34
- 33
- 32

Find the remainder when 3^{2013} is divided by 13.

N is a positive integer.

When N is divided by 3, the quotient is Q_{1} with remainder 1.

When Q_{1} is divided by 4, the quotient is Q_{2} with remainder 1.

When Q_{2} is divided by 5, the quotient is Q_{3} with remainder 1.

If Q_{1}, Q_{2}, and Q_{3} are positive integers, find the smallest possible value for N that will make all of this work.