last two digit of 123^(!123)

• If gcd(a,M) == 1 then
  a^ phi(M) % M = 1
  lets us consider M = 100
  phi(100) = 40
  123^40 % 100 = 1
  
  123! is multiple of 40.
  So 123^(123!) = 1
  
• 10 years agoHelpfull: Yes(0) No(2)
• 01 is the answer
  last 2 digit of 23^1 =23
  last 2 digit of 23^2 =29
  last 2 digit of 23^3 =67
  last 2 digit of 23^1 =23
  last 2 digit of 23^4 =41
  
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  last 2 digit of 23^20 =01
  last 2 digit of 23^21 =23
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  so 123! is multiple of 20
  therefore last 2 digit of 23^(123!) = 01
  
  
• 10 years agoHelpfull: Yes(0) No(0)
• 123^4*even no!
  for last two digit (23^4)^even no!
  =41^even no!
  =01
  so ans is 01
• 10 years agoHelpfull: Yes(0) No(0)
• how do we know tthat 123!is even @rakesh
  
• 10 years agoHelpfull: Yes(0) No(0)