Find the units digit for the sum 13^25+4^81+5^411Find the units digit for the sum 13^25+4^81+5^411Find the units digit for the sum 13^25+4^81+5^411Find the units digit for the sum 13^25+4^81+5^411Find

Find the units digit for the sum 13^25+4^81+5^411

Find the units digit for the sum 13^25+4^81+5^411

• “Powers of 3 go: 3, 9, 7, 1, 3, 9, 7, 1, ... with a period of 4. 
  25 mod 4 = 1 
  So the units digit of 13^25 is 3. 
  

• Powers of 4 go: 4, 6, 4, 6 ... with period 2. 
  81 mod 2 = 1 
  so the units digits of 4^81 is 4. 
  

• Powers of 5 always end in 5.

• So 3 + 4 + 5 = 12 
  and the units digits is 2.”