Melody

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Melody  Feb 11, 2022
 #74
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Heureka 3/8/15

http://web2.0calc.com/questions/how-come-30-99-61-100-is-divisible-by-31#r4

 

\small{\text{$30 \equiv - 1 \pmod {31}$}}\\

\small{\text{ and $61 \equiv - 1 \pmod {31}$}}\\\\

\small{\text{$(-1)^{99} + (-1)^{100} \stackrel{?}\equiv 0 \pmod{31}$}}\\\\

\small{\text{$-1 + 1 \equiv 0 \pmod{31}$}}\\\\

 

OUTPUT

$$\small{\text{$30 \equiv - 1 \pmod {31}$}}\\
\small{\text{ and $61 \equiv - 1 \pmod {31}$}}\\\\
\small{\text{$(-1)^{99} + (-1)^{100} \stackrel{?}\equiv 0 \pmod{31}$}}\\\\
\small{\text{$-1 + 1 \equiv 0 \pmod{31}$}}\\\\$$

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\stackrel{?}\equiv

OUTPUT

$$\stackrel{?}\equiv$$

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Aug 4, 2015
 #5
avatar+118723 
+5
Aug 4, 2015