Let x be a positive integer, what is the remainder when 4^(2x+5)+3 is divided by 5? Choose the most appropriate option
A) 2 B) 3 C) 4 D) 1 E) 5
For: (4^(2x+5)+3)/5   Let n = 2x + 5   4^n   4^1 = 4   4^2 = 16   4^3 = 64   4^4 = 256, last digit pattern repeats 4, 6, 4, 6, ....   Rule: x^(m+n) = (x^m)(x^n)   (4^(2x))(4^5)   Rule: x^(mn) = (x^m)^n   (4^2)(4^x)(4^5) =&gt; Now, (6)(4)(4) + 3 = (6) + 3 =&gt; Finally, 9/5 and remainder is 4.   Answer: 4
<result>C</result>
Let x be a positive integer, what is the remainder when 4^(2x+5)+3 is divided by 5?