Question

If \[\ x^2_{11}= y_{11}\] AND \[\ x^2_{10}=y_{10}\]
Then find all possible values of x and y

Answer 1

\[\{(0,0), (1,1)\}\]

Answer 2

Yes that is correct........ what about others

Answer 3

(11, 11)

Answer 4

(11,121)

Answer 5

So, will there be finite number of solutions or infinite ?

Answer 6

(2, 4), (3, 9)

infinite maybe..,

Answer 7

Is there any approach to do this type of calculation?

Answer 8

i see few more solutions, not sure if some clean approach exists calling @mukushla


(10, 100)
(11, 121)
(12, 144)
(13, 169)
(20, 400)
(21, 441)
(22, 484)
(30, 900)
(31, 961)

Answer 9

looks like it works if we restrict the digits to 1,2,3 for x.

for exampple, below value for x works :

(\1231233333332111111113333333332222111233333333222312\)

not sure if the solutions can come frm other variants