1541^1041 + 1671^2356 . find last two digits?

• by checking the periodicity of the last two digits of each no.
  for ex- periodicity of 41 in 1541= 5
  periodicity of 71 in 1671= 10
  therefore, 1041%5= 1 and 2356%10= 6
  hence, 41^1 + 71^6(=last 2 digits=21)=62
• 12 years agoHelpfull: Yes(19) No(0)
• 62,as the unit digit is 1
• 12 years agoHelpfull: Yes(5) No(6)
• @utkarsha periodicity of 1741 would be 6
  and ans would be 41^3+71^6=42
• 12 years agoHelpfull: Yes(1) No(5)
• (1541)^1041 + (1671)^2356
  (1541)^1041 + (5041)^1178
  cyclicity of 41 is 5.. so..
  (1541)^1 + (5041)^3
  (41)^1 + (41)^3
  41 + 21
  last two digit is 62.
• 12 years agoHelpfull: Yes(1) No(0)
• 1 raised to any power will give 1 as unit digit
  To find the digit in 10th place,
  10th digit in base*unit digit in power
  1541^1041+1671^2356
  so,
  41+21=62
  last two digit=62
• 9 years agoHelpfull: Yes(0) No(0)
• Any number whose unit digit is 1 will always give 1 as unit digit if it is multiplied by itself any number of times.
  
  So both 1541^1041 and 1671^2356 will have 1 at its unit place.
  
  Now to calculate the ten’s place there is a short trick. (This is applicable only in the case of number with unit digit as 1)
  
  Multiply the ten’s place digit of the base with the unit place digit of power.
  
  In 1541^1041 the ten’s place digit of the base is 4 and unit place digit of the power is 1. Multiply 4 x 1 which gives 4. This will be the ten’s place of 15411041.
  
  So the last two digits of 1541^1041 is 41.
  
  Now in 1671^2356 the ten’s place digit of the base is 7 and unit place digit of the power is 6. Multiply 7 x 6 which gives 42.The unit digit of this product which is 2 is the ten’s place digit of 1671^2356.
  
  So the last two digits of 1671^2356 is 21.
  
  As a result the last two digits of 1541^1041 + 1671^2356 = 41 + 21 = 62
• 8 years agoHelpfull: Yes(0) No(0)
• people there is one more easy trick to solve this:
  1541^1041 is the first function
  first we multiply unit digit of 1541 i.e 1 with unit digit of 1041 i.e again 1..so we get 1..which is the unit digit of the ans of 1541^1041 ...
  now for the tens place of 1541^1041 we multiply 4 of 1541 with unit digit of 1041 we get 4..
  so the ans of 1051^1041 is 4&1 i.e 41....
  similarly for 1671^2356 we repeat the above process ..first we take unit digit of 1671 i.e 1
  next we multiply 7 of 1671 and 6 of 2356 i.e 7*6=42...from 42 we only take 2 for the tens place of the ans of 1671^2356 so we get 21 as last two digits..
  now finally we add 21+41(last two digits of 1541^1041)= 62 is the ans..
• 8 years agoHelpfull: Yes(0) No(0)