MAT246H1 Lecture Notes - Composite Number, Natural Number, Prime Number

Let n be a natural number. (a) Then 4^n + 15n - 1 is divisible by nine. (b) If n is odd, then n^2 has a remainder of one when divided by eight. Let x, y, z elementof Z so that x^2 + y^2 = z^2. Show that five is a factor of xyz.

If x is the remainder when a multiple of 4 is divided by 6, and y is the remainder when a multiple of 2 is divided by 3, what is the greatest possible value of x + y? 2 3 5 6 9