2個整數既square相差404...............

Let the two integers as A and B

A^2 - B^2 = 404
(A-B)(A+B) = 404 (by different of 2 squres)
(A-B)(A+B) = 2 x 202 or 4 x 101

for case of (A-B)(A+B) = 2 x 202,

A - B = 2............(1)

and A+B=202..............(2)

(2) - (1)
2B=202 - 2 = 200
B = 100
A = 102

for case of (A-B)(A+B) = 4 x 101

A - B = 4 ................(3)

and A+B = 101...............(4)

(2) - (1)
2B = 101 - 4 = 97
B = 48.5 (it is not an answer, as A and B must be integer)

Ans.: The two numbers are 100 and 102.

2007-03-11 23:30:30 補充：
sorry, typofor case of (A-B)(A B) = 4 x 101A - B = 4 ................(3)and A B = 101...............(4)(4) - (3)2B = 101 - 4 = 97B = 48.5 (it is not an answer, as A and B must be integer)Ans.: The two numbers are 100 and 102.

102同100

pascal program:

program qa;
uses wincrt;
var
i,j:longint;
begin

for i:=1 to 1000 do
for j:=1 to 1000 do
if i*i-j*j=404 then writeln(i,j);
end.