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Divide years by 5
Posted: Fri Jan 18, 2019 6:58 pm
by samiul_samin
$S=2018^{2019}-2019^{2018}$
What is the remainder if we divide $S$ by $5$?
Re: Divide years by 5
Posted: Fri Jan 18, 2019 7:15 pm
by samiul_samin
Hint
Python Code
Answer
Solution
$2018^2\equiv-1(mod 5)$
$2018^{2018}\equiv-1(mod 5)$
$2018^{2019}\equiv-3\equiv2(mod 5)$...(1)
$2019^2\equiv1(mod 5)$
$2019^{2018}\equiv1(mod 5)$ ...(2)
$2018^{2019}-2019^{2018}\equiv1(mod 5)$...(1)-(2)
Source
Re: Divide years by 5
Posted: Wed Jan 23, 2019 2:37 pm
by Safwan
this one was easy.simple with mod.
Re: Divide years by 5
Posted: Wed Jan 23, 2019 4:28 pm
by samiul_samin
Safwan wrote: ↑Wed Jan 23, 2019 2:37 pm
this one was easy.simple with mod.
But it was impossible for those who dosen't know Modular arithmatic!