`1992^1993 + 1994^1995`
`= 1992^1992. 1992 + 1994^1995`
`= (1992^3)^664. 1992 + 1994^1995`
$\text{We have:}$
`1992^3 vdots 7`
`=> (1992^3)^664. 1992 vdots 7`
`1994 vdots 7`
`=> 1994^1995 vdots 7`
`<=> (1992^3)^664. 1992 + 1994^1995 vdots 7`
`<=> 1992^1993 + 1994^1995 vdots 7`
`<=> 1992^1993 + 1994^1995 equiv 0(mod 7)`
$\text{Hence,}$ `0` $\text{is the remainder of division}$ `(1992^1993 + 1994^1995) ÷ 7`
