Z {\displaystyle \mathbb {Z} } - מספר שלם.
9 n + 1 + 2 6 n + 1 11 = Z {\displaystyle {\frac {9^{n+1}+2^{6n+1}}{11}}=\mathbb {Z} }
9 n + 1 + 2 6 n + 1 11 = Z 9 2 + 1 + 2 6 + 1 11 = Z 19 = Z √ {\displaystyle {\begin{aligned}&{\frac {9^{n+1}+2^{6n+1}}{11}}=\mathbb {Z} \\&{\frac {9^{2+1}+2^{6+1}}{11}}=\mathbb {Z} \\&19=\mathbb {Z} \surd \\\end{aligned}}}
9 k + 1 + 2 6 k + 1 11 = Z {\displaystyle {\frac {9^{k+1}+2^{6k+1}}{11}}=\mathbb {Z} }
9 k + 2 + 2 6 k + 7 11 = Z 9 k + 1 ∗ 9 + 2 6 k + 1 ∗ 2 6 11 = Z 9 k + 1 ∗ 9 + 2 6 k + 1 ∗ 64 11 = Z 9 k + 1 ∗ 9 + 2 6 k + 1 ∗ ( 9 + 55 ) 11 = Z 9 ( 9 k + 1 + 2 6 k + 1 ) 11 + 55 ∗ 2 6 k + 1 11 = Z Z + 5 ∗ 6 k + 1 {\displaystyle {\begin{aligned}&{\frac {9^{k+2}+2^{6k+7}}{11}}=\mathbb {Z} \\&{\frac {9^{k+1}*9+2^{6k+1}*2^{6}}{11}}=\mathbb {Z} \\&{\frac {9^{k+1}*9+2^{6k+1}*64}{11}}=\mathbb {Z} \\&{\frac {9^{k+1}*9+2^{6k+1}*(9+55)}{11}}=\mathbb {Z} \\&{\frac {9(9^{k+1}+2^{6k+1})}{11}}+{\frac {55*2^{6k+1}}{11}}=\mathbb {Z} \\&\mathbb {Z} +5*^{6k+1}\\\end{aligned}}}
הטענה נכונה עבור כל n טבעי, ע"פ שלושת שלבי האינדוקציה.
