[tex] 9^7+3^{12}=3^{14}+3^{12}=3^{12}(3^2+1)=3^{12}\cdot10=3^{10}\cdot3^2\cdot10=3^{10}\cdot90 [/tex]
[tex] 25^9+5^{17}=5^{18}+5^{17}=5^{17}(5+1)=5^{17}\cdot 6=5^{16}\cdot5\cdot6=5^{16}\cdot30 [/tex]
It is prove that,
[tex]9^{7}+3^{12}[/tex] is divisible by 90.
[tex]25^9+5^{17}[/tex] is divisible by 30.
[tex]9^{7}+3^{12}[/tex] can be written as,
[tex]9^{7}+3^{12}=(3^{2})^{7}+3^{12}=3^{14}+3^{12} =3^{12}(3^{2} +1)=3^{12}*10=3^{10}*90[/tex]
Therefore, [tex]9^{7}+3^{12}[/tex] is divisible by 90.
[tex]25^9+5^{17}[/tex] can be written as,
[tex]25^9+5^{17}=5^{18} +5^{17}=5^{17}(5+1)=5^{16}*30[/tex]
Therefore, [tex]25^9+5^{17}[/tex] is divisible by 30.
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