These are stumping me for some odd reason... 1. Find the remainder of upon division by 9. 2. Determine with explanation, whether there exists an integer n such that is divisible by 151. (Note that 151 is prime)
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Hello, Aryth! 1. Find the remainder of upon division by 9. Since , then: . has a remainder of 2. Then: . has a remainder of We find that: . . . . and has remainder 1. Hence: .
Would anyone be able to help with the second one?
Originally Posted by Aryth Would anyone be able to help with the second one? well, it's quite easy: since the equation has no solution and thus, obviously, cannot have any solution either.
Originally Posted by NonCommAlg well, it's quite easy: since the equation has no solution and thus, obviously, cannot have any solution either. another way: suppose has a solution. then but, since by Fermat's little theorem contradiction!
I seriously appreciate the help.
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