## Problem Of The Week 44

**FInd the number of pairs (x,y) of integers 0<x<y such that sqrt(x)+sqrt(y)=sqrt(1984)**

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**FInd the number of pairs (x,y) of integers 0<x<y such that sqrt(x)+sqrt(y)=sqrt(1984)**

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Written by Implex

October 5, 2008 at 10:52 am

Posted in Number Thoery, Problem of the week

Tagged with Number Theory, Problem of the week

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991 pairs

1,(1983)^2 to (991)^2,(993)^2

tyroOctober 5, 2008 at 12:02 pm

pairs can be [1,1983], [2,1982]…..[1984,1]. {for sqrt {x} and sqrt{y}}

but y>x, so, sqrt{y}>sqrt{x}. so, pairs are till before{991,991}

hence, there are 990 pairs for root{y} and root{x} . and there fore for x and y too.

qwertyOctober 5, 2008 at 2:28 pm

sorry there was an error in question

kindly try again !

outtimedOctober 5, 2008 at 4:19 pm

Is the answer 3?

AmitOctober 5, 2008 at 5:16 pm

yeah !! it is 3

outtimedOctober 5, 2008 at 5:26 pm

(1,7) (2,6) (3,5)

each number in each pair multiplied by sqrt(31)

tyroOctober 6, 2008 at 11:49 am

yaar, we have to give (x,y) pairs. so there are 6 pairs.

3 others are (7,1) ,(6,2) , (5,3). correct me if i am wrong.

yodhaOctober 20, 2008 at 3:36 pm

no the answer would still be three because x must be less than y

ALDecember 17, 2008 at 1:15 am