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
11881001090=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
52=3
105=5
1710=7
2617=9

Posted by Lisa
on 20050615 12:58:50 