InterviewSolution
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InterviewSolution
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Prove that if `xa n dy`are odd positive integers, then `x^2+y^2`is even but not divisible by 4. |
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Answer» Let x=2m+1 and y=2m+3 are odd integers, for every positive integers, for every positive integer m, Then, `x^(2)+y^(2)(2m+1)^(2)+(2m+3)^(2)` `=4m^(2) =(2m+1)^(2)+(2m+3)^(2)` `=4m^(2)+1+4m+4m^(2)+9+12m [therefore (a+b)^(2)=a^(2)+2ab+b^(2)]` `=8m^(2)+16m+10="even"` `=2(4m^(2)+8m+5) or 4(2m^(2)+4m+2)+1` Hence, `x^(2)+y^(2)` is even for every positive integer m but not divisible by 4. |
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