Math Problem:
What is the last digit of 17 raised to the 17th power?
What is the last digit of 17 raised to the 17th power?
Reflection:
The patterns of this problem can be expressed in the language of modular arithmetic. Modular arithmetic is a system of arithmetic for integers, which considers the remainder. In modular arithmetic, numbers "wrap around" upon reaching a given fixed quantity (this given quantity is known as the modulus) to leave a remainder. Finding the last digit of a positive integer is the same as finding the remainder of that number when divided by 10. In general, the last digit of a power in base “n” is its remainder upon division by “n.” For decimal numbers, we compute (mod 10).
The patterns of this problem can be expressed in the language of modular arithmetic. Modular arithmetic is a system of arithmetic for integers, which considers the remainder. In modular arithmetic, numbers "wrap around" upon reaching a given fixed quantity (this given quantity is known as the modulus) to leave a remainder. Finding the last digit of a positive integer is the same as finding the remainder of that number when divided by 10. In general, the last digit of a power in base “n” is its remainder upon division by “n.” For decimal numbers, we compute (mod 10).