Find the reminder when 5^103 is divided by 13

Question

Use binomial theorem

Answer 1

5^103/13 leaves what number as a remainder ?

625/13=48 R1

625*625=390,625/13=30,048 R1

625*625*625=244,140,625 and 244,140,625/13=18,780,048 R1

from the pattern, 5^100=625^25 and 625^25/13 will leave a remainder of 1

this leaves 5*5*5 divided by 13 to determine the remainder

125/13=9 R8

in addition...

625*125/13=6009 R8

625*625*125/13=48,828,125/13=3,756,009 R8

5^3/13=125/13=9 R8

the conclusion is that 5^103/13 leaves a remainder of 8

Answer 2

                       Hi Natarajan.....

                                                     My handheld calculator gives me this answer...

 

          5^103           

      __________

           13                             

 

 

       = 9.86 x E71   divided by  13   = 7.59 x E70  =Answer   

 

              I will work on it more

 

                   Oscar Ahumada       

 

                      2/6/16