Real Analysis: Proving mn=1 Implies m & n = ±1

[johnjuwax]

Prove or disprove that if m and n are integers such that mn = 1 then either m= 1 & n = 1 or else m = -1 & n = -1.

 

[friend]

Prove or disprove that if m and n are integers such that mn = 1 then either m= 1 & n = 1 or else m = -1 & n = -1.

If mn=1, then m/1=1/n. But for n an integrer, then m is a fraction. The only way both are integers is if n=1 so that m=1, or if n=-1 so that m=-1.

 

[hamster143]

It follows from the fact that, if m>1, then 0<n<1, and if m<-1, then -1<n<0. Therefore we have three options left to check, m=-1, 0, 1.