Question

If an integer is a square and cube simultaniously then what is its form

Answer 1

If n^2 is simultaneously a cube, n≡a3≡−1,0,1(mod7) na3101mod7 and a square n≡t2≡0,1,4,2(mod7) nt20142mod7 Therefore n^2 is either 7kor 7k+1