Show that if u is an odd integer then the equation x

2. Show that if u is an odd integer, then the equation x 2 + x - u = 0 has no solution
that is an integer.
3. Show that for any x that is an integer, if ( x
2
- 1) is not divisible by 3, then x is
divisible by 3.
Hint: Any integer is either a multiple of 3, or a multiple of 3 plus 1, or a multiple
of 3 plus 2; i.e. m = 3k, or m = 3k + 1, or m = 3k + 2, for some k)
2

4. if a 2 + b 2 = c 2 , then a + b ≥ c , where a, b, & c are all non-negative integers
3