Q- What is the remainder when 1+2+2[tex]^{2}[/tex]+...+2[tex]^{219}[/tex] is divided by 5.(adsbygoogle = window.adsbygoogle || []).push({});

Solution: 2[tex]^{0}[/tex]=1 mod5

2[tex]^{1}[/tex]=2 mod5

2[tex]^{2}[/tex]=4 mod5

2[tex]^{3}[/tex]=3 mod5

2[tex]^{4}[/tex]=1 mod5

Now I take (1,2,4,3) to be a set numbers. Since the summation goes to 219, there are a total of 220/4 = 55 sets. So I add 1+2+4+3= 10 and 10*55 = 550 <- my answer.

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# Modular Arithematic-see if my answer is correct

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