Question

Show that 3(7^204 +7^202 +7^200)+7(3^204 +3^200)−(210)is divisible 10 .

Answer 1

Given:

$\bold{\frac{(7^{204} +7^{202} +7^{200})+7(3^{204} +3^{200})-(210)}{10}}$

To find:

value=?

Solution:

$\bold{\frac{(7^{204} +7^{202} +7^{200})+7(3^{204} +3^{200})-(210)}{10}}$

$=\frac{2.511887373744577e+172+7202+7200+7(3^{204}+3^{200})-210}{10}$

$=\frac{2.511887373744577e+172+5.126300762744035e+170+7200+7(3^{204}+3^{200})-210}{10}$

$=\frac{2.5631503813720173e+172+7200+7(3^{204}+3^{200})-210}{10}\\\\=\frac{2.5631503813720173e+172+1.0461838291314358e+169+7(3^{204}+3^{200})-210}{10}\\\\=\frac{2.5641965652011488e+172+7(3^{204}+3^{200})-210}{10}$

$=\frac{2.5641965652011488e+172+7(2.1514733098945854e+97+3^{200})-210}{10}\\\\=\frac{2.5641965652011488e+172+7(2.1514733098945854e+97+2.6561398887587478e+95)-210}{10}\\\\=\frac{2.5641965652011488e+172+(7)(2.178034708782173e+97)-210}{10}\\\\=\frac{2.5641965652011488e+172+1.524624296147521e+98-210}{10}$

$=\frac{2.5641965652011488e+172-210}{10}\\\\=\frac{2.5641965652011488e+172}{10}\\\\=\frac{1.2820982826005744e+172}{5}$