Problem Solving

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

taneja.niks wrote: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

3 repeats its last digit after every cycles, so when we divide 3^(8n+3) by remainder will always be 3, therefore last digit of the expression 3^(8n+3) would be 7, and last digit of the whole expression would be 3^(8n+3)+2=9, we know that remainder of a number when divided by 5 depends upon its last digit, for e.g. if 43 is divided by 5 remainder will be 3, similarly here remainder will be 9/5=4 hence answer should be E