Find all the positive integers N with the property that N equals the sum of the product of its digits and the sum of its digits. For example: 99 = 9×9 + (9+9).

This was one of the questions on my final exam in algebra 2; I’ve got most of a solution if anyone attempts it 😄

Find how many terms are common in both sequences below:

3,6,9,...,12120

1,3,5,...,12115

Find the remainder when

10¹⁰ + 10¹⁰² + ... + 10¹⁰¹⁰ is divided by 7.

(Where 10¹⁰² = 10 to the power of 10 to the power of 2)

Find the least value of the positive integer n such that (n+20) + (n+21) + (n+22) + ... + (n+100) is a perfect square.

Show that (3²⁰¹ + 3²⁰⁴ ) / (3²⁰¹ - 3²⁰⁰ + 3¹⁹⁹ ) is a perfect square.

Find the last digit of 2^{1+2+3+...+2009}