If m is an integer, which of the following is always true ?
1) m^2 - 1 is non - negative.
2) m(m + 1) is divisible by 3.
3) m(m ^ 2 + 1) is divisible by 4.
4) m^2 when divided by 3 leaves remainder 0 or 1 (but never 2).
5) If m < 0, then -m < - m^2
Please help in solving this problem.
1) m^2 - 1 is non - negative.
2) m(m + 1) is divisible by 3.
3) m(m ^ 2 + 1) is divisible by 4.
4) m^2 when divided by 3 leaves remainder 0 or 1 (but never 2).
5) If m < 0, then -m < - m^2
Please help in solving this problem.
Govind
