Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
120a + 36b = 12.10a + 12.3b = 12.\left( {10a + 3b} \right)\,\, \vdots \,\,12\\
2,\\
{5^7} - {5^6} + {5^5} = {5^5}.\left( {{5^2} - {5^1} + 1} \right) = {5^5}.\left( {25 - 5 + 1} \right) = {5^5}.21\,\, \vdots \,\,21\\
3,\\
{4^{39}} + {4^{40}} + {4^{41}} = {4^{39}}.\left( {1 + {4^1} + {4^2}} \right) = {4^{39}}.\left( {1 + 4 + 16} \right)\\
= {4^{39}}.21 = {4^{38}}.4.3.7 = {4^{38}}.3.28\,\, \vdots \,\,28\\
4,\\
{5^{2003}} + {5^{2002}} + {5^{2001}} = {5^{2001}}.\left( {{5^2} + {5^1} + 1} \right) = {5^{2001}}.\left( {25 + 5 + 1} \right)\\
= {5^{2001}}.31\,\, \vdots \,\,31\\
5,\\
{7^6} + {7^5} + {7^4} = {7^4}.\left( {{7^4} + 7 + 1} \right) = {7^4}.\left( {49 + 7 + 1} \right) = {7^4}.57\,\, \vdots \,\,57
\end{array}\)
