Question

Let X and Y be positive integers such that X^2 + 3X + Y^2 = 404.
What is the value of X + Y^3?

Find all possible solutions.

Thanks! :)

Answer 1

I ran a simple GW-Basic program

10 FOR X = 1 TO 25
20 FOR Y = 1 TO 25
30 IF (X*X + 3*X + Y*Y) = 404 THEN PRINT X,Y
40 NEXT Y
50 NEXT X

and it gave me values of x and y that worked, they were ...

1 20
13 14
16 10
17 8

so x + y^3 could be 8001, 2757, or 81