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x and y are a pair of positive integers such that both their sum and d

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Re: x and y are a pair of positive integers such that both their sum and d [#permalink]
Is there any easier way to get the pairs ?
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x and y are a pair of positive integers such that both their sum and d [#permalink]
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ManjariMishra wrote:
Is there any easier way to get the pairs ?

hi Manjari,

let s=perfect square
x+y=s1
x-y=s2
2x=s1+s2→
x=(s1+s2)/2
because x is integer, sum of squares must be even
so s1 and s2 must be either both even or both odd
there are 4 perfect even squares<100
so possible even pairs=(4*3)/2=6
there are 5 perfect odd squares<100
so possible odd pairs=(5*4)/2=10
6+10=16 total possible pairs

I hope this helps,
gracie
x and y are a pair of positive integers such that both their sum and d [#permalink]
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