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Find the sum of the orders mod 83 over all elements of the set \($\{1,2,3,\ldots,82\}$\). (If multiple elements have the same order, add that term multiple times.)

 May 9, 2019

Best Answer 

 #1
avatar+22574 
+2

Find the sum of the orders mod 83 over all elements of the \(set \{1,2,3,\ldots,82\}\).

(If multiple elements have the same order, add that term multiple times.)

 

 ord83(1)=1
 ord83(2)=82
 ord83(3)=41
 ord83(4)=41
 ord83(5)=82
 ord83(6)=82
 ord83(7)=41
 ord83(8)=82
 ord83(9)=41
 ord83(10)=41
 ord83(11)=41
 ord83(12)=41
 ord83(13)=82
 ord83(14)=82
 ord83(15)=82
 ord83(16)=41
 ord83(17)=41
 ord83(18)=82
 ord83(19)=82
 ord83(20)=82
 ord83(21)=41
 ord83(22)=82
 ord83(23)=41
 ord83(24)=82
 ord83(25)=41
 ord83(26)=41
 ord83(27)=41
 ord83(28)=41
 ord83(29)=41
 ord83(30)=41
 ord83(31)=41
 ord83(32)=82
 ord83(33)=41
 ord83(34)=82
 ord83(35)=82
 ord83(36)=41
 ord83(37)=41
 ord83(38)=41
 ord83(39)=82
 ord83(40)=41
 ord83(41)=41
 ord83(42)=82
 ord83(43)=82
 ord83(44)=41
 ord83(45)=82
 ord83(46)=82
 ord83(47)=82
 ord83(48)=41
 ord83(49)=41
 ord83(50)=82
 ord83(51)=41
 ord83(52)=82
 ord83(53)=82
 ord83(54)=82
 ord83(55)=82
 ord83(56)=82
 ord83(57)=82
 ord83(58)=82
 ord83(59)=41
 ord83(60)=82
 ord83(61)=41
 ord83(62)=82
 ord83(63)=41
 ord83(64)=41
 ord83(65)=41
 ord83(66)=82
 ord83(67)=82
 ord83(68)=41
 ord83(69)=41
 ord83(70)=41
 ord83(71)=82
 ord83(72)=82
 ord83(73)=82
 ord83(74)=82
 ord83(75)=41
 ord83(76)=82
 ord83(77)=41
 ord83(78)=41
 ord83(79)=82
 ord83(80)=82
 ord83(81)=41
 ord83(82)=2


 sum = 4923

 

laugh

 May 10, 2019
 #1
avatar+22574 
+2
Best Answer

Find the sum of the orders mod 83 over all elements of the \(set \{1,2,3,\ldots,82\}\).

(If multiple elements have the same order, add that term multiple times.)

 

 ord83(1)=1
 ord83(2)=82
 ord83(3)=41
 ord83(4)=41
 ord83(5)=82
 ord83(6)=82
 ord83(7)=41
 ord83(8)=82
 ord83(9)=41
 ord83(10)=41
 ord83(11)=41
 ord83(12)=41
 ord83(13)=82
 ord83(14)=82
 ord83(15)=82
 ord83(16)=41
 ord83(17)=41
 ord83(18)=82
 ord83(19)=82
 ord83(20)=82
 ord83(21)=41
 ord83(22)=82
 ord83(23)=41
 ord83(24)=82
 ord83(25)=41
 ord83(26)=41
 ord83(27)=41
 ord83(28)=41
 ord83(29)=41
 ord83(30)=41
 ord83(31)=41
 ord83(32)=82
 ord83(33)=41
 ord83(34)=82
 ord83(35)=82
 ord83(36)=41
 ord83(37)=41
 ord83(38)=41
 ord83(39)=82
 ord83(40)=41
 ord83(41)=41
 ord83(42)=82
 ord83(43)=82
 ord83(44)=41
 ord83(45)=82
 ord83(46)=82
 ord83(47)=82
 ord83(48)=41
 ord83(49)=41
 ord83(50)=82
 ord83(51)=41
 ord83(52)=82
 ord83(53)=82
 ord83(54)=82
 ord83(55)=82
 ord83(56)=82
 ord83(57)=82
 ord83(58)=82
 ord83(59)=41
 ord83(60)=82
 ord83(61)=41
 ord83(62)=82
 ord83(63)=41
 ord83(64)=41
 ord83(65)=41
 ord83(66)=82
 ord83(67)=82
 ord83(68)=41
 ord83(69)=41
 ord83(70)=41
 ord83(71)=82
 ord83(72)=82
 ord83(73)=82
 ord83(74)=82
 ord83(75)=41
 ord83(76)=82
 ord83(77)=41
 ord83(78)=41
 ord83(79)=82
 ord83(80)=82
 ord83(81)=41
 ord83(82)=2


 sum = 4923

 

laugh

heureka May 10, 2019

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