# Number theory: finding integer solution to an equation

by mtayab1994
Tags: equation, integer, number, solution, theory
P: 328
 Quote by mtayab1994 Which new definitions m=x-y???
Don't backtrack. We have defined new variables ##m## and ##n##; the formula translates into those variables as shown; now you need to understand what ##m^2=3n## tells you about ##m##.
P: 555
 Quote by Joffan Don't backtrack. We have defined new variables ##m## and ##n##; the formula translates into those variables as shown; now you need to understand what ##m^2=3n## tells you about ##m##.
Well there are 3 cases:

Case 1: if m Ξ 0(mod3) then m^2 Ξ 0(mod3)

Case 2: if m Ξ 1(mod3) then m^2 Ξ 1(mod3)

Case 3: if m Ξ 2(mod3) then m^2 Ξ 4(mod3) with is m^2 Ξ 1(mod3)

So that means that m^2=3n . So that means the when m is divided by 3 you get either a remainder of 0,1, or 2 am i right?
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P: 10,896
 Quote by mtayab1994 Well there are 3 cases: Case 1: if m Ξ 0(mod3) then m^2 Ξ 0(mod3) Case 2: if m Ξ 1(mod3) then m^2 Ξ 1(mod3) Case 3: if m Ξ 2(mod3) then m^2 Ξ 4(mod3) with is m^2 Ξ 1(mod3)
Looks good.

 So that means that m^2=3n . So that means the when m is divided by 3 you get either a remainder of 0,1, or 2 am i right?
How did you come up with that conclusion based on what you wrote above?
 P: 328 What is the value of ##3n## mod 3?
P: 555
 Quote by Joffan What is the value of ##3n## mod 3?
3n mod 3 means that 3n=3k so that means 3k equals the multiples of 3 which are 3n.

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