1.5^20+5^7/7=? Reminderis…………

2. 12^82/72=? Remonder…………
3.11^99/18=? Reminder………
give its short cut

• 1) 5^20+5^7/7
  5^20 mod 7 + 5^7 mod 7
  Since 5 nd 7 are co-primes, we can use Euler's theorem
  E(7) = 6
  So 5^E(7) = 1
  5^20 mod 7 => (5^6)^3 * 5^2 mod 7
  1 * 25 mod 7 = 4
  Similarly 5^7 mod 7 => 5^6 * 5 mod 7
  1 * 5 mod 7 = 5
  Now 4 + 5 mod 7
  9 mod 7 = 2
  Ans : 2
  
  2) 12^82 mod 72
  (12^2)^41 mod 72
  144^41 mod 72
  (72*2 + 0)^41 mod 72
  0^41 mod 72 = 0
  Ans : 0
  
  3) 11^99 mod 18
  (18 - 7)^99 mod 18
  (-7)^99 mod 18
  E(18) = 6
  (-7^6)^16 * (-7)^3 mod 18
  1 * (-343) mod 18
  -1 mod 18
  (-1+18) mod 18 = 17
  Ans : 17
  
• 9 years agoHelpfull: Yes(3) No(9)
• 5^20+5^7
  5,25,125,625,3125,15625,78125,390625,1953125,9765625,,,,here last 3 digit in same sequence 625 and 125,even ana odd position soooo
  5^20,, 20 even so last digit 625 and 7 odd mean 125
  125+625=7507=rem 1... may be not sure
  
• 9 years agoHelpfull: Yes(1) No(3)