Question

j^3 = 61 + i^6
Find all the integer solution of i and j.

Answer 1

One is i=2 and j=5

Answer 2

What about other?

Answer 3

\[j^3-(i^2)^3=61\]
\[(j-i^2)(j^2+ij+i^2)=61\]
61 is prime so 61(1) are the only factors
hence \[j-i^2=1,j^2+ij+i^2=61\]

Answer 4

Looks like 4 solution.

Answer 5

but we imgore the fact that it can be vise versa 1(61)