Prove that if m² is 4k+3 then m is 4k+3

[CollectiveRocker]

I'm given the statement: if m^2 is of the form 4k+3, then m is of the form 4k+3. I don't even know how to begin proving this. I'm guessing by contraposition.

 

[robert Ihnot]

You put this already under general math

 

[mathwonk]

good guess. if m is not of form 4k+3 thern m is of form 4k, 4k+1, or 4k+2. see what that gives.

 

[CollectiveRocker]

Please explain what you mean.

 

[mathwonk]

all integers m are of one of the three forms 4k, 4k+1, 4k+2, or 4k+3, since when you divide an integer by 4, you get a remainder which is either 0,1,2, or 3.

 

[eNathan]

The only way that m^2 = 4k+3 AND m = 4k+3 is if m=1

Is this what you meant?

 

[MathStudent]

This problem has been posted (and answered) 3 times. for anyone who wants to respond this question, please go to the link below

https://www.physicsforums.com/showthread.php?t=63215