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 Discussion Forums -> This Post 15 points    (3    in 3 votes )   [?]

1994=(x+y)^2+3x+y=(x+y)^2+2(x+y)+1+(x-y)-1=(x+y+1)^2-(y-x+1)

1995+y-x=(x+y+1)^2

RHS is a square of integer number, we must find it by trial such that y-x is as small as possible integer.

nearest square numbers to 1995 are 44^2=1936 and 45^2=2025    (since x and y have to be integers)

using x+y+1=45    ---(1)

y-x=2025-1995=30   ---(2)

from eq. 1 and 2

y=37, and x=7

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