có: \(1890^2\equiv0\left(mod7\right)\)
\(\Rightarrow\left(1890^2\right)^{965}\equiv0\left(mod7\right)\) (1)
Ta có: \(1945^2\equiv1\left(mod7\right)\)
\(\left(1945^2\right)^{987}\equiv1^{987}\equiv1\left(mod7\right)\)
\(\Rightarrow1945^{1975}\equiv1945^{1974}\cdot1945\equiv1\cdot6\equiv6\left(mod7\right)\) (2)
Từ (1), (2)
\(\Rightarrow1890^{1930}+1945^{1975}+1\equiv0+6+1\equiv7⋮7\left(đpcm\right)\)