if n is a positive integer,what is the remainder when 3^(8n+3) + 2 is divided by a.0 b.1 c.2 d.3 e.4need detailed explanation!thx

if n is a positive integer,what is the remainder when 3^(8n+3) + 2 is divided by a.0 b.1 c.2 d.3 e.4need detailed explanation!thx
if n is a positive integer,what is the remainder when 3^(8n+3) + 2 is divided by
a.0 b.1 c.2 d.3 e.4
need detailed explanation!thx

if n is a positive integer,what is the remainder when 3^(8n+3) + 2 is divided by a.0 b.1 c.2 d.3 e.4need detailed explanation!thx
如果N是正整数,当3^(8n+3) + 2 被5整除的余数是多少?
8n+3 when divided by 4 gives a remainder of 3.
Since powers of 3 make cycles of 4 i.e.3,9,27,81,..3,..9,..7,..1,..3
so 38n+3 will have 7 at the units place.
when 2 is added we get 9 at the units place.
Thus when divided by 5 we get 4 as remainder.
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1、被5除究竟余数为多少，主要是看那个数字的个位数，而N又是一个不具体的正整数，那么我们就需要知道个位数的规律

3^1 3^2 3^3 3^4
3^5 3^6 3^7 3^8
个位数3 9 7 1

2、随着3的次方变化，以个位数“3 9 7 1”循环，8n+3究竟能...

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1、被5除究竟余数为多少，主要是看那个数字的个位数，而N又是一个不具体的正整数，那么我们就需要知道个位数的规律

3^1 3^2 3^3 3^4
3^5 3^6 3^7 3^8
个位数3 9 7 1

2、随着3的次方变化，以个位数“3 9 7 1”循环，8n+3究竟能做4的几次循环呢？
8n+3除以4=2n……3, 会移动到第三个数，即以7结尾

3、所以3^8n+3 的个位数为7，加上2，即9，除以5，余数为4

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