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3^(8n+3)+2 = 3^8n*3^3+2. 3 ^( anything to the form 4n where n=1,2,3,4) will end with 1. (8n=4*2n) 3^3 ends with 7 so ....1*....7=no. ending with 7. so (no. ending with 7) +2=no. ending with 9. when divided by 5,remaider is 4

arjtryarjtry has already given a great explanation!

arjtryarjtry wrote:

3^(8n+3)+2 = 3^8n*3^3+2. 3 ^( anything to the form 4n where n=1,2,3,4) will end with 1. (8n=4*2n) 3^3 ends with 7 so ....1*....7=no. ending with 7. so (no. ending with 7) +2=no. ending with 9. when divided by 5,remaider is 4

3^(8n+3)+2 = 3^8n*3^3+2. 3 ^( anything to the form 4n where n=1,2,3,4) will end with 1. (8n=4*2n) 3^3 ends with 7 so ....1*....7=no. ending with 7. so (no. ending with 7) +2=no. ending with 9. when divided by 5,remaider is 4

This method works with a denominator of 5 with any number that ends with a 7 (as noted above): (27+2)/5 = 5 remainder of 4 (37+2)/5 = 7 remainder of 4 (47+2)/5 = 9 remainder of 4 ---> all remainders of 4

but what if the denominator was 6: (27+2)/6 = 4 remainder of 5 (37+2)/6 = 6 remainder of 3 ---> you get 2 different remainders. Am I missing something in the method above??
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Factorials were someone's attempt to make math look exciting!!!

If n is a positive integer, what is the remainder when \(3^{8n+3} + 2\) is divided by 5?

A. 0 B. 1 C. 2 D. 3 E. 4

Show the quickest way to solve this question.

Thks

i took n=1, \(3^{8n+3} + 2\) = (27(3^8)+2)/5 = 5+((2(3^8)+2)/5) 3^8=6561 => 5+(((6561*2)+2 )/2)=> remainder = 4

Hence this is the method i used.Here there is no question of what can be the remainder its just what is the remnainder which means take any value of n and solve
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