Homework

Problem 1. Can a number written with one hundred 0's, one hundred 1's and one hundred 2's be a perfect square? Hint: This number is divisible by 3 but not by 9.

Problem 2.Find the solutions in natural numbers of the equation a) x²-y²=31, and b) x²-y²=303. Hint: x²-y²=(x-y)(x+y).

Problem 3. Given natural numbers a, b and c such that a+b+c is divisible by 6, prove that is also divisible by 6.

Problem 4. Find the greatest common divisor of 1381955 and 690713.