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You are not logged in. #76 20090112 22:05:39
Re: 5 Star Questions
You got it. What you want to prove is that 5 divides , not . And yes, to show that an integer is divisible by 30, it suffices to show that it is divisible by 2, 3 and 5. Since 2, 3 and 5 are all prime, a number that is divisible by all of them will be divisible by their product. Fermat’s little theorem states that if is a prime and is an integer coprime with (in other words does not divide ) then #77 20090112 22:47:02#78 20090113 00:26:12
Re: 5 Star QuestionsAnswer to #36: Character is who you are when no one is looking. #79 20090113 01:46:06
Re: 5 Star Questions#37. What is the value of ? #38.Find the number of prime factors in . #39. What is the value of ? Character is who you are when no one is looking. #80 20090113 13:23:19
Re: 5 Star QuestionsBy the way …
In general, the factors don’t have to be prime; they only need to be relatively prime. For example, to prove that a number is divisible by 24, it suffices to show that it is divisible by both 3 and 8. Although 8 is not a prime, we have gcd(3,8) = 1, and that’s good enough. Any number that is divisible by 3 and 8 will be divisible by 24. #81 20090113 13:28:18#82 20090113 16:35:51
Re: 5 Star QuestionsAnswer to #37: Character is who you are when no one is looking. #83 20090114 00:03:35#84 20090114 00:23:00
Re: 5 Star QuestionsAnswer to #37: Character is who you are when no one is looking. #85 20090114 01:47:56
Re: 5 Star Questions#40. What is the value of #41. Find the value of a+b if . #42. If what is the value of ? #43. Find the value of (1) (2) (3) (4) #44. Which is the largest four digit number which is a perfect cube? Character is who you are when no one is looking. #86 20090114 02:07:21
Re: 5 Star Questions#45. What is the value of (2) ? (3) ? (4) ? #46. What is the value of (1) ? (2) ? (3) ? (4) ? Character is who you are when no one is looking. #87 20090114 06:24:17#88 20090114 17:17:10
Re: 5 Star QuestionsAnswers to #40, #43(1), #43(2), #43(3), #45(2), #45(3), #45(4), #46(1), #46(2), #46(3), and #46(4): Character is who you are when no one is looking. #89 20090115 00:15:44
Re: 5 Star Questions#47. Find the least fraction which when added to the expression given below would result in a whole number. #48. A postman goes from a place P to another place Q, his speeds during the first onethird, second onethird and the third onethird of the distance being 4, 5 and 4½ kilometers per hour rsepectively. He returns from Q to P at the speed of 4 kilometers per hour. Find his average speed throughout the journey. #49. If S = 1³ + 2³ + 3³ + 4³ + ...... n³ , what is the minimum value of n such that S>5000? #50. A train after travelling 50 kilometers meets with an accident and then travels at of its former speed and arrives at the destination 35 minutes late. Had the accident occured 24 kilometers after it did, the train would have reached the destination only 23 minutes late. Find the speed of the train and the distance. Character is who you are when no one is looking. #90 20090115 13:05:52#92 20090115 18:02:38
Re: 5 Star QuestionsAnswers to #47, #48, #49, and #50: Character is who you are when no one is looking. #93 20090115 23:06:12
Re: 5 Star Questions#51. If a+b : b+c : c+a = 6 : 7 : 8 and a + b + c = 14, what is the value of c? Character is who you are when no one is looking. #94 20090115 23:31:17#95 20090115 23:42:50
Re: 5 Star QuestionsAnswer to #49: Character is who you are when no one is looking. #96 20090116 00:14:33#97 20090116 00:47:38
Re: 5 Star QuestionsAnswers to #49, #51, #52, #53, and #54: Character is who you are when no one is looking. #98 20090117 02:33:07
Re: 5 Star Questions#57. If tan (A+B) = p and tan (AB) = q, find tan 2B in terms of p and q. Character is who you are when no one is looking. #99 20090117 07:53:55#100 20090118 03:15:26
Re: 5 Star QuestionsAnswers to #57, #58, #359, and #60: Character is who you are when no one is looking. 