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

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- Sep 22nd 2012, 09:12 AMPetrusnumber theory
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

- Sep 22nd 2012, 09:51 AMMaxJasperRe: number theory
- Sep 22nd 2012, 10:01 AMPetrusRe: number theory
Sorry but i did not get it with 5^31

- Sep 22nd 2012, 11:26 AMSorobanRe: number theory
Hello, Petrus!

You are on the right track . . .

Quote:

$\displaystyle \text{What is the remainder when }11^{30}+5^{31}-6\text{ is divided by 24?}$

$\displaystyle 11^{30} \;=\; (11^2)^{15} \;=\;(121)^{15} \;\equiv\; 1^{15}\text{ (mod 24)} \;\equiv\;1\text{ (mod 24)}$

$\displaystyle 5^{31} \;=\;5\cdot5^{30} \;=\;5(5^2)^{15} \;=\;5(25)^{15} \;\equiv\; 5(1)^{15}\text{ (mod 24)} \;=\; 5\text{ (mod 24)}$

Therefore: .$\displaystyle 11^{30} + 5^{31} - 6 \;\equiv\;1 + 5 - 6 \text{ (mod 24)} \;\equiv\;0\text{ (mod 24)}$

The remainder is zero.

- Sep 22nd 2012, 11:39 AMPetrusRe: number theory
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