i prob post on wrong sector but idk where i should post it, sorry
the quest is :
Which (positive) residual obtained when 11^30+5^31-6 divided by 24?
i have got this far
11^30=(11^2)^15=121^15 ==1^15 (mod 24)
i cant solve rest :S
Hello, Petrus!
You are on the right track . . .
$\displaystyle \text{What is the remainder when }11^{30}+5^{31}-6\text{ is divided by 24?}$
$\displaystyle 11^{30} \;=\; (11^2)^{15} \;=\;(121)^{15} \;\equiv\; 1^{15}\text{ (mod 24)} \;\equiv\;1\text{ (mod 24)}$
$\displaystyle 5^{31} \;=\;5\cdot5^{30} \;=\;5(5^2)^{15} \;=\;5(25)^{15} \;\equiv\; 5(1)^{15}\text{ (mod 24)} \;=\; 5\text{ (mod 24)}$
Therefore: .$\displaystyle 11^{30} + 5^{31} - 6 \;\equiv\;1 + 5 - 6 \text{ (mod 24)} \;\equiv\;0\text{ (mod 24)}$
The remainder is zero.
ty sorban ur was clearly and i did understand :P
maxjasper sorry u did not have alot space kinda confused me :P
i was thinking like soo but thought it was wrong