what are the last two digits of 3^1997

• Considering only last two digits:
  3^0= 01
  3^1= 03
  3^2= 09
  3^3= 27
  3^4= 81
  3^5= 43
  3^6= 29
  3^7= 87
  3^8= 61
  3^9= 83
  3^10= 49
  3^11= 47
  3^12= 41
  3^13= 23
  3^14= 64
  3^15= 07
  3^16= 21
  3^17= 63
  3^18= 89
  3^19= 67
  3^20= 01 (same as 3^0=01)
  
  As we can see, Pattern repeats itself every 20th exponent.
  
  Now 1997/20= 99.85
  
  Take only integer part and multiply by 20 = 99*20 = 1980
  
  Subtract it from 1997 => 1997-1980 = 17
  
  Hence, the last two digits will be the same as that of 3^17=63
• 10 years agoHelpfull: Yes(4) No(2)