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Choose the main technique to prove the following statement:
For every integer m,
m(m+1)(m+2) is an integer multiple of 3.
Choose the main technique to prove the following statement:
The sum of two rational numbers is rational.
Choose the main technique to prove the following statement:
If n is an integer and
2 \leq n \leq 4, then
n^2 \geq 2^n.
To prove: If n^2 is odd, then
n is odd.
In the following statements, first, determine whether a statement shall be used in the proof, then, if the statement shall be used, determine the right sequence to present it.
To prove: If n is odd, then
n^2 is odd.
In the following statements, first, determine whether a statement shall be used in the proof, then, if the statement shall be used, determine the right sequence to present it.
Choose the main technique to prove the following statement.
If 5n^2+6n+7 is odd, then
n is even.
Choose the main technique to prove the following statement.
If n is even, then
n^2 is even.
Choose the main technique to prove the following statement.
n is even if and only if
5n^2+6n+7 is odd.
Choose the main technique to prove the following statement.
\sqrt{3} is irrational.
Choose the main technique to prove the following statement.
If n^2 is even, then
n is even.