There are pairs of numbers whose sum and product are perfect squares. For instance, 5 + 20 = 25 and 5 x 20 = 100.

If the smallest number of such a pair is 1090, what is the smallest possible value of the other number? No computers!!

I looked at other smaller numbers whose sum and product are perfect squares and i came up with

2+2=4 (2^2)           2x2=4
10+90=100 (10^2)   10x90=900
17+272=289 (17^2)  17x272=4624
26+650=676 (26^2)   26x650=16900

These three and the one in the question the sum of the two number is the perfect square of the lowest number so I decided to try this with 1090.

1090^2= 1188100
1188100-1090=1187010

1090+1187010=1188100 (1090^2)
1090X1187010=1293840900 (35970^2)

I'm not sure if 1187010 is the smallest number though.

An observation with the other pairs:
2 and 2
5 and 20
10 and 90
17 and 272
26 and 650

5-2=3
10-5=5
17-10=7
26-17=9

Posted by Lisa on 2005-06-15 12:58:50