Decide whether the following statement is true or false. If it is true, show that it is true, making your argument as general as possible. If it is false, disprove it by finding a counterexample.
For all integers a and b, if a is congruent to b (mod 35), then a^2 is congruent to b^2 (mod 7).
Decide whether the following statement is true or false.
If it is true, show that it is true, making your argument as general as possible.
If it is false, disprove it by finding a counterexample.
. .
Given: .
This means: .
. . So we have: .
Square both sides: .
. . And we have:. . . . . a multiple of 7
Therefore: .