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Solve-for-all-integer-x-y-Z-x-2-y-2-19-

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Question Number 22561 by Bruce Lee last updated on 20/Oct/17
Solve for all integer x,y ∈Z x^2 +y^2 =19
Solveforallintegerx,y∈Zx2+y2=19
Answered by $@ty@m last updated on 20/Oct/17
Case−1. Let x=0 ⇒y=(√(19))∉Z Case−2. Let x=±1 ⇒y=(√(18))∉Z Case−3. Let x=±2 ⇒y=(√(15))∉Z Case−4. Let x=±3 ⇒y=(√(10))∉Z Case−5. Let x=±4 ⇒y=(√3)∉Z ⇒ No solution for x,y∈Z
Case−1.Letx=0⇒y=19∉ZCase−2.Letx=±1⇒y=18∉ZCase−3.Letx=±2⇒y=15∉ZCase−4.Letx=±3⇒y=10∉ZCase−5.Letx=±4⇒y=3∉Z⇒Nosolutionforx,y∈Z

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